Edit Profile (opens in new tab) Schneider, Guido Compute Distance To: Compute Author ID: schneider.guido Published as: Schneider, Guido; Schneider, G. Homepage: https://www.iadm.uni-stuttgart.de/team/Schneider-00003/ External Links: MGP · dblp · GND Documents Indexed: 136 Publications since 1992, including 4 Books 9 Contributions as Editor Reviewing Activity: 26 Reviews Co-Authors: 75 Co-Authors with 107 Joint Publications 1,475 Co-Co-Authors all top 5 Co-Authors 37 single-authored 21 Uecker, Hannes 14 Düll, Wolf-Patrick 12 Pelinovsky, Dmitry Efimovich 11 Chirilus-Bruckner, Martina 9 Wayne, Clarence Eugene 8 Chong, Christopher 8 Zimmermann, Dominik 5 Mielke, Alexander 4 Groves, Mark D. 4 Lescarret, Vincent 3 Blank, Carsten 3 de Rijk, Björn 3 Kunze, Markus 3 Sandstede, Björn 3 Scheel, Arnd 3 Schratz, Katharina 2 Bauer, Roman 2 Baumstark, Simon 2 Blömker, Dirk 2 Doelman, Arjen 2 Eckmann, Jean-Pierre 2 Fukuizumi, Reika 2 Gallay, Thierry 2 Häcker, Tobias 2 Kashani, Kourosh Sanei 2 Melbourne, Ian 2 Pego, Robert L. 2 Sunny, Danish Ali 1 Bianchi, Luigi Amedeo 1 Bitzer, Jochen 1 Bollerman, Peter 1 Brand, Thomas 1 Breindl, Norbert 1 Bridges, Thomas J. 1 Busch, Kurt 1 Craig, Walter 1 Cummings, Patrick 1 Daub, Markus 1 Dohnal, Tomáš 1 Dörfler, Willibald 1 Gauß, Nicole 1 Gilg, Steffen 1 Griesemer, Marcel 1 Guillod, Julien 1 Haas, Tobias 1 Hărăguş-Courcelle, Mariana 1 Hermann, Alina 1 Hilder, Bastian 1 James, Guillaume 1 Kevrekidis, Panayotis G. 1 Kirchhoff, Andreas 1 Kirrmann, Pius 1 Klumpp, Maximilian 1 Kostianko, Anna 1 Lechleiter, Armin 1 Liero, Matthias 1 MacKay, Robert Sinclair 1 Maier-Paape, Stanislaus 1 Maier, Daniela 1 Marzuola, Jeremy L. 1 Matthies, Karsten 1 Melcher, Andreas 1 Müller, Johannes 1 Peterhof, Daniela 1 Plum, Michael 1 Prill, Oskar 1 Rapti, Zoi 1 Reichelt, Sina 1 Schmid, Jochen 1 Seelbach, Thorsten 1 Stuart, Charles Alexander 1 Theil, Florian 1 Thomas, Marita 1 Tkeshelashvili, Lasha 1 van Harten, Aart 1 Wand, Michael 1 Wieners, Christian 1 Wittwer, Peter 1 Ziegra, Andreas 1 Zink, Oliver all top 5 Serials 11 Journal of Differential Equations 8 Communications in Mathematical Physics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Journal of Nonlinear Science 6 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 6 Mathematical Methods in the Applied Sciences 6 Mathematische Nachrichten 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 Journal of Mathematical Analysis and Applications 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 NoDEA. Nonlinear Differential Equations and Applications 4 Archive for Rational Mechanics and Analysis 4 Physica D 4 SIAM Journal on Mathematical Analysis 3 Applicable Analysis 3 Nonlinearity 3 Oberwolfach Reports 2 Communications on Pure and Applied Mathematics 2 Letters in Mathematical Physics 2 European Journal of Applied Mathematics 2 Journal of Dynamics and Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Discrete and Continuous Dynamical Systems. Series B 2 Discrete and Continuous Dynamical Systems. Series S 1 Wave Motion 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Indiana University Mathematics Journal 1 Memoirs of the American Mathematical Society 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Applied Mathematics Letters 1 Asymptotic Analysis 1 Differential and Integral Equations 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Applied Mathematics 1 Electronic Journal of Differential Equations (EJDE) 1 Journal of Difference Equations and Applications 1 Journal of Applied Analysis 1 Communications in Applied Analysis 1 Chaos 1 Annales Henri Poincaré 1 Nonlinear Analysis. Real World Applications 1 Graduate Studies in Mathematics 1 Oberwolfach Seminars 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Advances in Mathematical Physics 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 131 Partial differential equations (35-XX) 47 Fluid mechanics (76-XX) 25 Dynamical systems and ergodic theory (37-XX) 12 Optics, electromagnetic theory (78-XX) 9 General and overarching topics; collections (00-XX) 7 Ordinary differential equations (34-XX) 5 Quantum theory (81-XX) 3 Mechanics of deformable solids (74-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 2 Biology and other natural sciences (92-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 113 Publications have been cited 1,396 times in 613 Documents Cited by ▼ Year ▼ The validity of modulation equations for extended systems with cubic nonlinearities. Zbl 0786.35122Kirrmann, Pius; Schneider, Guido; Mielke, Alexander 79 1992 Attractors for modulation equations on unbounded domains – existence and comparison. Zbl 0833.35016Mielke, Alexander; Schneider, Guido 78 1995 The long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1034.76011Schneider, Guido; Wayne, C. Eugene 76 2000 The dynamics of modulated wave trains. Zbl 1179.35005Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 56 2009 Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation. Zbl 0861.35107Schneider, Guido 45 1996 The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006Schneider, Guido; Wayne, C. Eugene 38 2002 Validity and limitation of the Newell-Whitehead equation. Zbl 0844.35120Schneider, Guido 37 1995 Error estimates for the Ginzburg-Landau approximation. Zbl 0805.35125Schneider, Guido 36 1994 Propagation of hexagonal patterns near onset. Zbl 1044.37049Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 35 2003 Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model. Zbl 0970.35126Schneider, Guido; Wayne, C. Eugene 32 2000 Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances. Zbl 1075.35080Schneider, Guido 29 2005 Bifurcations of standing localized waves on periodic graphs. Zbl 1387.35556Pelinovsky, Dmitry; Schneider, Guido 28 2017 Justification of modulation equations for hyperbolic systems via normal forms. Zbl 0890.35082Schneider, Guido 26 1998 Justification of the nonlinear Schrödinger equation in spatially periodic media. Zbl 1109.35104Busch, Kurt; Schneider, Guido; Tkeshelashvili, Lasha; Uecker, Hannes 24 2006 Nonlinear diffusive stability of spatially periodic solutions – abstract theorem and higher space dimensions –. Zbl 0907.35015Schneider, Guido 23 1998 Diffusive mixing of periodic wave trains in reaction-diffusion systems. Zbl 1298.35108Sandstede, Björn; Scheel, Arnd; Schneider, Guido; Uecker, Hannes 22 2012 Kawahara dynamics in dispersive media. Zbl 0977.35123Schneider, Guido; Wayne, C. Eugene 22 2001 Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian 22 2011 A new estimate for the Ginzburg-Landau approximation on the real axis. Zbl 0803.35139Schneider, G. 20 1994 KP description of unidirectional long waves. The model case. Zbl 1015.76015Gallay, Thierry; Schneider, Guido 20 2001 Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. Zbl 1186.35207Pelinovsky, Dmitry; Schneider, Guido 19 2010 Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178Schneider, Guido; Wayne, C. Eugene 19 2011 Nonlinear stability of Taylor vortices in infinite cylinders. Zbl 0916.76022Schneider, Guido 18 1998 The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions. Zbl 1344.35138Schneider, Guido; Sunny, Danish Ali; Zimmermann, Dominik 18 2015 Nonlinear PDEs. A dynamical systems approach. Zbl 1402.35001Schneider, Guido; Uecker, Hannes 17 2017 Bifurcating fronts for the Taylor-Couette problem in infinite cylinders. Zbl 0922.35015Hărağuş-Courcelle, Mariana; Schneider, Guido 16 1999 Global existence results for pattern forming processes in infinite cylindrical domains – applications to 3D Navier-Stokes problems. Zbl 0933.35025Schneider, Guido 15 1999 Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. Zbl 1334.35313Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene 15 2016 Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Zbl 1162.47059Pelinovsky, Dmitry; Schneider, Guido; MacKay, Robert S. 15 2008 Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model. Zbl 1194.35362Düll, Wolf-Patrick; Schneider, Guido 14 2006 Long-time persistence of Korteweg-de Vries solitons as transient dynamics in a model of inclined film flow. Zbl 1174.35102Pego, Robert L.; Schneider, Guido; Uecker, Hannes 14 2007 Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. Zbl 1248.35182Chirilus-Bruckner, Martina; Chong, Christopher; Prill, Oskar; Schneider, Guido 14 2012 Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Zbl 0988.35158Schneider, Guido; Uecker, Hannes 14 2001 Validity of the NLS approximation for periodic quantum graphs. Zbl 1367.35156Gilg, Steffen; Pelinovsky, Dmitry; Schneider, Guido 14 2016 Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Zbl 1132.41344Pelinovsky, Dmitry; Schneider, Guido 13 2007 Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. Zbl 1177.35216Dohnal, Tomáš; Pelinovsky, Dmitry; Schneider, Guido 13 2009 Rigorous justification of the short-pulse equation. Zbl 1268.35089Pelinovsky, Dmitry; Schneider, Guido 11 2013 Comparison of inertial manifolds and application to modulated systems. Zbl 0957.35025Mielke, A.; Schneider, G.; Ziegra, A. 11 2000 The validity of generalized Ginzburg-Landau equations. Zbl 0874.35050Schneider, Guido 11 1996 Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations. Zbl 0803.35140Schneider, Guido 11 1994 The long wave limit for a Boussinesq equation. Zbl 0911.35105Schneider, Guido 11 1998 Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation. Zbl 0940.35179Schneider, Guido 11 1998 Justification of the Ginzburg-Landau approximation in case of marginally stable long waves. Zbl 1209.35010Häcker, Tobias; Schneider, Guido; Zimmermann, Dominik 11 2011 The stochastic Landau equation as an amplitude equation. Zbl 1004.60074Blömker, D.; Maier-Paape, S.; Schneider, G. 11 2001 Analyticity of Ginzburg-Landau modes. Zbl 0832.35021Schneider, Guido 10 1995 Hopf bifurcation in spatially extended reaction-diffusion systems. Zbl 0899.58048Schneider, G. 10 1998 Modulating pulse solutions for quasilinear wave equations. Zbl 1078.35074Groves, Mark D.; Schneider, Guido 10 2005 Non-linear stability of modulated fronts for the Swift-Hohenberg equation. Zbl 0994.35057Eckmann, J.-P.; Schneider, G. 10 2002 Phase dynamics in the real Ginzburg-Landau equation. Zbl 1057.35064Melbourne, Ian; Schneider, Guido 10 2004 Justification of the Ginzburg-Landau approximation for an instability as it appears for Marangoni convection. Zbl 1285.35114Schneider, Guido; Zimmermann, Dominik 9 2013 Validity of Whitham’s equations for the modulation of periodic traveling waves in the NLS equation. Zbl 1179.35305Düll, Wolf-Patrick; Schneider, Guido 9 2009 On the justification of the Ginzburg-Landau approximation. Zbl 0836.35147Bollerman, P.; van Harten, A.; Schneider, G. 9 1995 Modulating pulse solutions for a class of nonlinear wave equations. Zbl 0981.35041Groves, M. D.; Schneider, G. 9 2001 Breather solutions in periodic media. Zbl 1223.35234Blank, Carsten; Chirilus-Bruckner, Martina; Lescarret, Vincent; Schneider, Guido 9 2011 Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. Zbl 1041.35074Schneider, Guido; Uecker, Hannes 9 2003 Hopf bifurcation and exchange of stability in diffusive media. Zbl 1064.35021Brand, Thomas; Kunze, Markus; Schneider, Guido; Seelbach, Thorsten 9 2004 Bounds for the nonlinear Schrödinger approximation of the Fermi-Pasta-Ulam system. Zbl 1194.35427Schneider, Guido 8 2010 Justification of the NLS approximation for the KdV equation using the Miura transformation. Zbl 1417.37251Schneider, Guido 8 2011 Stable transport of information near essentially unstable localized structures. Zbl 1055.35021Gallay, Thierry; Schneider, Guido; Uecker, Hannes 8 2004 The amplitude equations for the first instability of electro-convection in nematic liquid crystals in the case of two unbounded space directions. Zbl 1116.76030Schneider, Guido; Uecker, Hannes 7 2007 On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Zbl 1252.35247Chong, Christopher; Pelinovsky, Dmitry E.; Schneider, Guido 7 2012 Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation. Zbl 0856.35060Mielke, Alexander; Schneider, Guido 7 1996 A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in \(\mathbb R^{3}\). Zbl 1153.37389Melcher, Andreas; Schneider, Guido; Uecker, Hannes 7 2008 Stability and diffusive dynamics on extended domains. Zbl 1004.35018Mielke, Alexander; Schneider, Guido; Uecker, Hannes 7 2001 Nonlinear stability of bifurcating front solutions for the Taylor-Couette problem. Zbl 0967.35109Eckmann, J.-P.; Schneider, G. 7 2000 Phase dynamics in the complex Ginzburg-Landau equation. Zbl 1059.35139Melbourne, Ian; Schneider, Guido 7 2004 Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401Schneider, Guido; Wayne, C. Eugene 7 2003 On the validity of 2D surface water wave models. Zbl 1096.76504Schneider, Guido; Wayne, C. Eugene 6 2002 Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an unbounded domain. Zbl 0929.76043Schneider, G. 6 1999 Justification of mean-field coupled modulation equations. Zbl 0880.35108Schneider, Guido 6 1997 On the interaction of NLS-described modulating pulses with different carrier waves. Zbl 1149.35392Chirilus-Bruckner, Martina; Schneider, Guido; Uecker, Hannes 5 2007 Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves. Zbl 1159.35066Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido; Uecker, Hannes 5 2008 NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms. Zbl 1311.35164Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 5 2015 Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation. Zbl 1315.35185Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 5 2014 Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity. Zbl 1280.35133Chong, Christopher; Schneider, Guido 4 2013 Some characterizations of the Taylor-Couette attractor. Zbl 1012.35011Schneider, Guido 4 1999 Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales. Zbl 1160.35052Groves, M. D.; Schneider, G. 4 2008 From the Klein-Gordon-Zakharov system to the Klein-Gordon equation. Zbl 1352.35072Daub, Markus; Schneider, Guido; Schratz, Katharina 4 2016 Justification of the equations for the resonant four wave interaction. Zbl 1100.76013Schneider, Guido; Zink, Oliver 3 2005 A waiting time phenomenon in pattern forming systems. Zbl 1190.35029Düll, Wolf-Patrick; Schneider, Guido 3 2009 The mathematics of light pulses in dispersive media. Zbl 1204.35002Schneider, Guido; Uecker, Hannes 3 2007 Detection of standing pulses in periodic media by pulse interaction. Zbl 1259.78030Chirilus-Bruckner, Martina; Schneider, Guido 3 2012 Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum. Zbl 1063.35029Kunze, M.; Schneider, G. 3 2004 Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves. Zbl 1360.76061Schneider, Guido 3 2016 Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times. Zbl 1058.76065Schneider, Guido; Uecker, Hannes 3 2003 Modulation equation and SPDEs on unbounded domains. Zbl 1435.35292Bianchi, Luigi Amedeo; Blömker, Dirk; Schneider, Guido 3 2019 Corrigendum: the long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1236.76016Schneider, Guido; Wayne, C. Eugene 2 2012 Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms. Zbl 1236.35122Häcker, Tobias; Schneider, Guido; Uecker, Hannes 2 2012 Interaction of modulated pulses in nonlinear oscillator chains. Zbl 1228.34026Schneider, Guido; Uecker, Hannes; Wand, Michael 2 2011 Aproximation and attractivity properties of the degenerated Ginzburg-Landau equation. Zbl 1117.35033Bitzer, Jochen; Schneider, Guido 2 2007 Exponential averaging for traveling wave solutions in rapidly varying periodic media. Zbl 1206.35146Matthies, Karsten; Schneider, Guido; Uecker, Hannes 2 2007 The validity of the KdV approximation in case of resonances arising from periodic media. Zbl 1241.35175Chong, Christopher; Schneider, Guido 2 2011 Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide. Zbl 1253.35173Lescarret, Vincent; Schneider, Guido 2 2012 Attractivity of the Ginzburg-Landau mode distribution for a pattern forming system with marginally stable long modes. Zbl 1341.35152Düll, Wolf-Patrick; Kashani, Kourosh Sanei; Schneider, Guido; Zimmermann, Dominik 2 2016 Moving gap solitons in periodic potentials. Zbl 1156.35465Pelinovsky, Dmitry; Schneider, Guido 2 2008 Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media. Zbl 1262.35169Lescarret, Vincent; Blank, Carsten; Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido 2 2009 A proof of validity for multiphase Whitham modulation theory. Zbl 1472.35332Bridges, Thomas J.; Kostianko, Anna; Schneider, Guido 2 2020 On the dynamics of the mean-field polaron in the high-frequency limit. Zbl 1436.35289Griesemer, Marcel; Schmid, Jochen; Schneider, Guido 2 2017 Justification of the 2D NLS equation for a fourth order nonlinear wave equation - quadratic resonances do not matter much in case of analytic initial conditions. Zbl 1333.35251Düll, Wolf-Patrick; Hermann, Alina; Schneider, Guido; Zimmermann, Dominik 2 2016 Nonlinear stability at the Eckhaus boundary. Zbl 1454.35361Guillod, Julien; Schneider, Guido; Wittwer, Peter; Zimmermann, Dominik 2 2018 A proof of validity for multiphase Whitham modulation theory. Zbl 1472.35332Bridges, Thomas J.; Kostianko, Anna; Schneider, Guido 2 2020 Global existence and decay in nonlinearly coupled reaction-diffusion-advection equations with different velocities. Zbl 1435.35198de Rijk, Björn; Schneider, Guido 1 2020 The monoatomic FPU system as a limit of a diatomic FPU system. Zbl 1442.35456Pelinovsky, Dmitry E.; Schneider, Guido 1 2020 Effective slow dynamics models for a class of dispersive systems. Zbl 1452.35014Baumstark, Simon; Schneider, Guido; Schratz, Katharina; Zimmermann, Dominik 1 2020 Modulation equation and SPDEs on unbounded domains. Zbl 1435.35292Bianchi, Luigi Amedeo; Blömker, Dirk; Schneider, Guido 3 2019 A model for the periodic water wave problem and its long wave amplitude equations. Zbl 1442.35322Bauer, Roman; Cummings, Patrick; Schneider, Guido 1 2019 The Korteweg-de Vries, Burgers and Whitham limits for a spatially periodic Boussinesq model. Zbl 1421.35319Bauer, Roman; Düll, Wolf-Patrick; Schneider, Guido 1 2019 Nonlinear stability at the Eckhaus boundary. Zbl 1454.35361Guillod, Julien; Schneider, Guido; Wittwer, Peter; Zimmermann, Dominik 2 2018 Bifurcations of standing localized waves on periodic graphs. Zbl 1387.35556Pelinovsky, Dmitry; Schneider, Guido 28 2017 Nonlinear PDEs. A dynamical systems approach. Zbl 1402.35001Schneider, Guido; Uecker, Hannes 17 2017 On the dynamics of the mean-field polaron in the high-frequency limit. Zbl 1436.35289Griesemer, Marcel; Schmid, Jochen; Schneider, Guido 2 2017 Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. Zbl 1334.35313Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene 15 2016 Validity of the NLS approximation for periodic quantum graphs. Zbl 1367.35156Gilg, Steffen; Pelinovsky, Dmitry; Schneider, Guido 14 2016 From the Klein-Gordon-Zakharov system to the Klein-Gordon equation. Zbl 1352.35072Daub, Markus; Schneider, Guido; Schratz, Katharina 4 2016 Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves. Zbl 1360.76061Schneider, Guido 3 2016 Attractivity of the Ginzburg-Landau mode distribution for a pattern forming system with marginally stable long modes. Zbl 1341.35152Düll, Wolf-Patrick; Kashani, Kourosh Sanei; Schneider, Guido; Zimmermann, Dominik 2 2016 Justification of the 2D NLS equation for a fourth order nonlinear wave equation - quadratic resonances do not matter much in case of analytic initial conditions. Zbl 1333.35251Düll, Wolf-Patrick; Hermann, Alina; Schneider, Guido; Zimmermann, Dominik 2 2016 The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions. Zbl 1344.35138Schneider, Guido; Sunny, Danish Ali; Zimmermann, Dominik 18 2015 NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms. Zbl 1311.35164Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 5 2015 Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation. Zbl 1315.35185Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 5 2014 Justification of leading order quasicontinuum approximations of strongly nonlinear lattices. Zbl 1307.35256Chong, Christopher; Kevrekidis, P. G.; Schneider, Guido 1 2014 Rigorous justification of the short-pulse equation. Zbl 1268.35089Pelinovsky, Dmitry; Schneider, Guido 11 2013 Justification of the Ginzburg-Landau approximation for an instability as it appears for Marangoni convection. Zbl 1285.35114Schneider, Guido; Zimmermann, Dominik 9 2013 Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity. Zbl 1280.35133Chong, Christopher; Schneider, Guido 4 2013 Diffusive mixing of periodic wave trains in reaction-diffusion systems. Zbl 1298.35108Sandstede, Björn; Scheel, Arnd; Schneider, Guido; Uecker, Hannes 22 2012 Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. Zbl 1248.35182Chirilus-Bruckner, Martina; Chong, Christopher; Prill, Oskar; Schneider, Guido 14 2012 On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Zbl 1252.35247Chong, Christopher; Pelinovsky, Dmitry E.; Schneider, Guido 7 2012 Detection of standing pulses in periodic media by pulse interaction. Zbl 1259.78030Chirilus-Bruckner, Martina; Schneider, Guido 3 2012 Corrigendum: the long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1236.76016Schneider, Guido; Wayne, C. Eugene 2 2012 Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms. Zbl 1236.35122Häcker, Tobias; Schneider, Guido; Uecker, Hannes 2 2012 Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide. Zbl 1253.35173Lescarret, Vincent; Schneider, Guido 2 2012 Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian 22 2011 Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178Schneider, Guido; Wayne, C. Eugene 19 2011 Justification of the Ginzburg-Landau approximation in case of marginally stable long waves. Zbl 1209.35010Häcker, Tobias; Schneider, Guido; Zimmermann, Dominik 11 2011 Breather solutions in periodic media. Zbl 1223.35234Blank, Carsten; Chirilus-Bruckner, Martina; Lescarret, Vincent; Schneider, Guido 9 2011 Justification of the NLS approximation for the KdV equation using the Miura transformation. Zbl 1417.37251Schneider, Guido 8 2011 Interaction of modulated pulses in nonlinear oscillator chains. Zbl 1228.34026Schneider, Guido; Uecker, Hannes; Wand, Michael 2 2011 The validity of the KdV approximation in case of resonances arising from periodic media. Zbl 1241.35175Chong, Christopher; Schneider, Guido 2 2011 Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. Zbl 1186.35207Pelinovsky, Dmitry; Schneider, Guido 19 2010 Bounds for the nonlinear Schrödinger approximation of the Fermi-Pasta-Ulam system. Zbl 1194.35427Schneider, Guido 8 2010 The dynamics of modulated wave trains. Zbl 1179.35005Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 56 2009 Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. Zbl 1177.35216Dohnal, Tomáš; Pelinovsky, Dmitry; Schneider, Guido 13 2009 Validity of Whitham’s equations for the modulation of periodic traveling waves in the NLS equation. Zbl 1179.35305Düll, Wolf-Patrick; Schneider, Guido 9 2009 A waiting time phenomenon in pattern forming systems. Zbl 1190.35029Düll, Wolf-Patrick; Schneider, Guido 3 2009 Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media. Zbl 1262.35169Lescarret, Vincent; Blank, Carsten; Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido 2 2009 Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Zbl 1162.47059Pelinovsky, Dmitry; Schneider, Guido; MacKay, Robert S. 15 2008 A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in \(\mathbb R^{3}\). Zbl 1153.37389Melcher, Andreas; Schneider, Guido; Uecker, Hannes 7 2008 Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves. Zbl 1159.35066Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido; Uecker, Hannes 5 2008 Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales. Zbl 1160.35052Groves, M. D.; Schneider, G. 4 2008 Moving gap solitons in periodic potentials. Zbl 1156.35465Pelinovsky, Dmitry; Schneider, Guido 2 2008 Long-time persistence of Korteweg-de Vries solitons as transient dynamics in a model of inclined film flow. Zbl 1174.35102Pego, Robert L.; Schneider, Guido; Uecker, Hannes 14 2007 Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Zbl 1132.41344Pelinovsky, Dmitry; Schneider, Guido 13 2007 The amplitude equations for the first instability of electro-convection in nematic liquid crystals in the case of two unbounded space directions. Zbl 1116.76030Schneider, Guido; Uecker, Hannes 7 2007 On the interaction of NLS-described modulating pulses with different carrier waves. Zbl 1149.35392Chirilus-Bruckner, Martina; Schneider, Guido; Uecker, Hannes 5 2007 The mathematics of light pulses in dispersive media. Zbl 1204.35002Schneider, Guido; Uecker, Hannes 3 2007 Aproximation and attractivity properties of the degenerated Ginzburg-Landau equation. Zbl 1117.35033Bitzer, Jochen; Schneider, Guido 2 2007 Exponential averaging for traveling wave solutions in rapidly varying periodic media. Zbl 1206.35146Matthies, Karsten; Schneider, Guido; Uecker, Hannes 2 2007 Justification of the nonlinear Schrödinger equation in spatially periodic media. Zbl 1109.35104Busch, Kurt; Schneider, Guido; Tkeshelashvili, Lasha; Uecker, Hannes 24 2006 Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model. Zbl 1194.35362Düll, Wolf-Patrick; Schneider, Guido 14 2006 Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances. Zbl 1075.35080Schneider, Guido 29 2005 Modulating pulse solutions for quasilinear wave equations. Zbl 1078.35074Groves, Mark D.; Schneider, Guido 10 2005 Justification of the equations for the resonant four wave interaction. Zbl 1100.76013Schneider, Guido; Zink, Oliver 3 2005 Local in time and space nonlinear stability of pulses in an unstable medium. Zbl 1106.76032Schneider, Guido; Pego, Robert L.; Uecker, Hannes 1 2005 Estimates for the KdV-limit of the Camassa-Holm equation. Zbl 1084.35074Kunze, Markus; Schneider, Guido 1 2005 Phase dynamics in the real Ginzburg-Landau equation. Zbl 1057.35064Melbourne, Ian; Schneider, Guido 10 2004 Hopf bifurcation and exchange of stability in diffusive media. Zbl 1064.35021Brand, Thomas; Kunze, Markus; Schneider, Guido; Seelbach, Thorsten 9 2004 Stable transport of information near essentially unstable localized structures. Zbl 1055.35021Gallay, Thierry; Schneider, Guido; Uecker, Hannes 8 2004 Phase dynamics in the complex Ginzburg-Landau equation. Zbl 1059.35139Melbourne, Ian; Schneider, Guido 7 2004 Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum. Zbl 1063.35029Kunze, M.; Schneider, G. 3 2004 Validity of the Ginzburg-Landau approximation in pattern forming systems with time periodic forcing. Zbl 1093.35035Breindl, Norbert; Schneider, Guido; Uecker, Hannes 1 2004 Propagation of hexagonal patterns near onset. Zbl 1044.37049Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 35 2003 Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. Zbl 1041.35074Schneider, Guido; Uecker, Hannes 9 2003 Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401Schneider, Guido; Wayne, C. Eugene 7 2003 Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times. Zbl 1058.76065Schneider, Guido; Uecker, Hannes 3 2003 The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006Schneider, Guido; Wayne, C. Eugene 38 2002 Non-linear stability of modulated fronts for the Swift-Hohenberg equation. Zbl 0994.35057Eckmann, J.-P.; Schneider, G. 10 2002 On the validity of 2D surface water wave models. Zbl 1096.76504Schneider, Guido; Wayne, C. Eugene 6 2002 Kawahara dynamics in dispersive media. Zbl 0977.35123Schneider, Guido; Wayne, C. Eugene 22 2001 KP description of unidirectional long waves. The model case. Zbl 1015.76015Gallay, Thierry; Schneider, Guido 20 2001 Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Zbl 0988.35158Schneider, Guido; Uecker, Hannes 14 2001 The stochastic Landau equation as an amplitude equation. Zbl 1004.60074Blömker, D.; Maier-Paape, S.; Schneider, G. 11 2001 Modulating pulse solutions for a class of nonlinear wave equations. Zbl 0981.35041Groves, M. D.; Schneider, G. 9 2001 Stability and diffusive dynamics on extended domains. Zbl 1004.35018Mielke, Alexander; Schneider, Guido; Uecker, Hannes 7 2001 Bifurcation analysis for a spatially extended random walk system in mathematical biology. Zbl 1084.35545Schneider, Guido; Müller, Johannes 1 2001 The long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1034.76011Schneider, Guido; Wayne, C. Eugene 76 2000 Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model. Zbl 0970.35126Schneider, Guido; Wayne, C. Eugene 32 2000 Comparison of inertial manifolds and application to modulated systems. Zbl 0957.35025Mielke, A.; Schneider, G.; Ziegra, A. 11 2000 Nonlinear stability of bifurcating front solutions for the Taylor-Couette problem. Zbl 0967.35109Eckmann, J.-P.; Schneider, G. 7 2000 Existence and stability of modulating pulse-solutions in a phenomenological model of nonlinear optics. Zbl 0954.35148Schneider, Guido 1 2000 Bifurcating fronts for the Taylor-Couette problem in infinite cylinders. Zbl 0922.35015Hărağuş-Courcelle, Mariana; Schneider, Guido 16 1999 Global existence results for pattern forming processes in infinite cylindrical domains – applications to 3D Navier-Stokes problems. Zbl 0933.35025Schneider, Guido 15 1999 Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an unbounded domain. Zbl 0929.76043Schneider, G. 6 1999 Some characterizations of the Taylor-Couette attractor. Zbl 1012.35011Schneider, Guido 4 1999 Justification of modulation equations for hyperbolic systems via normal forms. Zbl 0890.35082Schneider, Guido 26 1998 Nonlinear diffusive stability of spatially periodic solutions – abstract theorem and higher space dimensions –. Zbl 0907.35015Schneider, Guido 23 1998 Nonlinear stability of Taylor vortices in infinite cylinders. Zbl 0916.76022Schneider, Guido 18 1998 The long wave limit for a Boussinesq equation. Zbl 0911.35105Schneider, Guido 11 1998 Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation. Zbl 0940.35179Schneider, Guido 11 1998 Hopf bifurcation in spatially extended reaction-diffusion systems. Zbl 0899.58048Schneider, G. 10 1998 Justification of mean-field coupled modulation equations. Zbl 0880.35108Schneider, Guido 6 1997 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 681 Authors 72 Schneider, Guido 22 Pelinovsky, Dmitry Efimovich 21 Scheel, Arnd 20 Zumbrun, Kevin R. 18 Düll, Wolf-Patrick 16 Uecker, Hannes 15 Johnson, Mathew A. 13 Blömker, Dirk 13 Mielke, Alexander 11 Rodrigues, Luis Miguel 11 Sandstede, Björn 10 Dohnal, Tomáš 9 Bridges, Thomas J. 9 Noble, Pascal 8 Bambusi, Dario 8 Chirilus-Bruckner, Martina 8 de Rijk, Björn 8 Dovetta, Simone 8 Wayne, Clarence Eugene 8 Zelik, Sergey V. 8 Zimmermann, Dominik 7 Gao, Hongjun 7 Lannes, David 6 Barker, Blake 6 Coclite, Giuseppe Maria 6 Di Ruvo, Lorenzo 6 Jung, Soyeun 6 Kalisch, Henrik 6 Latushkin, Yuri 6 Pu, Xueke 6 Ratliff, Daniel J. 5 Beck, Margaret 5 Cholewa, Jan W. 5 Craig, Walter 5 Dlotko, Tomasz W. 5 Doelman, Arjen 5 Duan, Jinqiao 5 Gallay, Thierry 5 Guo, Boling 5 Haragus, Mariana 5 Herrmann, Michael 5 Israwi, Samer 5 Kühn, Christian 5 Matthies, Karsten 5 Mohammed, Wael W. 5 Sacchetti, Andrea 5 Schratz, Katharina 5 Sulem, Catherine 4 Adami, Riccardo 4 Bianchi, Luigi Amedeo 4 Bona, Jerry Lloyd 4 Chong, Christopher 4 Erbay, Husnuata A. 4 Erkip, Albert Kohen 4 Ghazaryan, Anna 4 Giannoulis, Johannes 4 Guo, Yanfeng 4 Guyenne, Philippe 4 James, Guillaume 4 Jaramillo, Gabriela 4 Jones, Christopher K. R. T. 4 Mederski, Jarosław 4 Paleari, Simone 4 Rademacher, Jens Diederich Michael 4 Sparber, Christof 4 Sun, Chunyou 4 Tentarelli, Lorenzo 4 Wright, J. Douglas 3 Bu, Charles 3 Choi, Yuncherl 3 Colin, Thierry 3 Dangelmayr, Gerhard 3 Duchêne, Vincent 3 Erbay, Saadet 3 Goh, Ryan N. 3 Groves, Mark D. 3 Ha, Taeyoung 3 Hairer, Martin 3 Hilder, Bastian 3 Hur, Vera Mikyoung 3 Kairzhan, Adilbek 3 Kevrekidis, Panayotis G. 3 Kusdiantara, Rudy 3 Liu, Huimin 3 Lloyd, David J. B. 3 Malomed, Boris A. 3 Marzuola, Jeremy L. 3 Masmoudi, Nader 3 Ogawa, Toshiyuki 3 Oprea, Iuliana 3 Penati, Tiziano 3 Rodríguez-Bernal, Aníbal 3 Rousset, Frédéric 3 Saut, Jean-Claude 3 Serra, Enrico 3 Sukhtayev, Alim 3 Susanto, Hadi 3 Tilli, Paolo 3 Totz, Nathan 3 Wolfrum, Matthias ...and 581 more Authors all top 5 Cited in 151 Serials 53 Journal of Differential Equations 44 Physica D 27 Archive for Rational Mechanics and Analysis 23 Journal of Nonlinear Science 22 Journal of Mathematical Analysis and Applications 20 Communications in Mathematical Physics 19 Nonlinearity 15 Discrete and Continuous Dynamical Systems 14 Journal of Dynamics and Differential Equations 13 Mathematical Methods in the Applied Sciences 12 Applicable Analysis 12 SIAM Journal on Mathematical Analysis 12 SIAM Journal on Applied Dynamical Systems 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Journal of Mathematical Physics 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Studies in Applied Mathematics 7 Communications in Partial Differential Equations 7 Chaos 6 Applied Mathematics and Computation 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Communications in Nonlinear Science and Numerical Simulation 6 Nonlinear Analysis. Real World Applications 6 Discrete and Continuous Dynamical Systems. Series S 5 Inventiones Mathematicae 5 Journal of Computational and Applied Mathematics 5 Transactions of the American Mathematical Society 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Communications on Pure and Applied Mathematics 4 Mathematische Nachrichten 4 NoDEA. Nonlinear Differential Equations and Applications 4 Annales Henri Poincaré 4 Water Waves 3 Computers & Mathematics with Applications 3 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 3 Journal of Computational Physics 3 Letters in Mathematical Physics 3 Wave Motion 3 Mathematics of Computation 3 Reviews in Mathematical Physics 3 Mathematics and Computers in Simulation 3 Quarterly of Applied Mathematics 3 Applied Mathematics Letters 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of Mathematical Fluid Mechanics 3 Discrete and Continuous Dynamical Systems. Series B 3 Communications on Pure and Applied Analysis 3 Multiscale Modeling & Simulation 3 Advances in Difference Equations 3 Boundary Value Problems 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Journal of Statistical Physics 2 Physics Letters. A 2 Chaos, Solitons and Fractals 2 Advances in Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Functional Analysis 2 Chinese Annals of Mathematics. Series B 2 Applied Numerical Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Asymptotic Analysis 2 European Journal of Applied Mathematics 2 Japan Journal of Industrial and Applied Mathematics 2 SIAM Journal on Applied Mathematics 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Physics of Fluids 2 Electronic Journal of Differential Equations (EJDE) 2 Journal of Inequalities and Applications 2 European Journal of Mechanics. B. Fluids 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Physics A: Mathematical and Theoretical 2 Advances in Mathematical Physics 2 Science China. Mathematics 2 Symmetry 1 International Journal of Control 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Biology 1 Physics Reports 1 Reviews of Modern Physics 1 Rocky Mountain Journal of Mathematics 1 Applied Mathematics and Optimization 1 Czechoslovak Mathematical Journal 1 Duke Mathematical Journal 1 Glasgow Mathematical Journal 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Ricerche di Matematica 1 Transactions of the Moscow Mathematical Society 1 Bulletin of the Korean Mathematical Society 1 Stochastic Analysis and Applications 1 Acta Applicandae Mathematicae 1 Journal of Scientific Computing 1 Applied Mathematical Modelling ...and 51 more Serials all top 5 Cited in 30 Fields 523 Partial differential equations (35-XX) 133 Fluid mechanics (76-XX) 126 Dynamical systems and ergodic theory (37-XX) 51 Ordinary differential equations (34-XX) 44 Numerical analysis (65-XX) 42 Optics, electromagnetic theory (78-XX) 41 Statistical mechanics, structure of matter (82-XX) 37 Quantum theory (81-XX) 23 Probability theory and stochastic processes (60-XX) 22 Mechanics of deformable solids (74-XX) 19 Operator theory (47-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 17 Mechanics of particles and systems (70-XX) 10 Difference and functional equations (39-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 Biology and other natural sciences (92-XX) 6 Functional analysis (46-XX) 5 Geophysics (86-XX) 4 Approximations and expansions (41-XX) 3 Combinatorics (05-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 2 Real functions (26-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Computer science (68-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year