Schneider, Guido

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 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
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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
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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
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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)

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 0786.35122
Kirrmann, Pius; Schneider, Guido; Mielke, Alexander
1992
Attractors for modulation equations on unbounded domains – existence and comparison. Zbl 0833.35016
Mielke, Alexander; Schneider, Guido
1995
The long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1034.76011
Schneider, Guido; Wayne, C. Eugene
2000
The dynamics of modulated wave trains. Zbl 1179.35005
Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido
2009
Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation. Zbl 0861.35107
Schneider, Guido
1996
The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006
Schneider, Guido; Wayne, C. Eugene
2002
Validity and limitation of the Newell-Whitehead equation. Zbl 0844.35120
Schneider, Guido
1995
Error estimates for the Ginzburg-Landau approximation. Zbl 0805.35125
Schneider, Guido
1994
Propagation of hexagonal patterns near onset. Zbl 1044.37049
Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido
2003
Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model. Zbl 0970.35126
Schneider, Guido; Wayne, C. Eugene
2000
Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances. Zbl 1075.35080
Schneider, Guido
2005
Bifurcations of standing localized waves on periodic graphs. Zbl 1387.35556
Pelinovsky, Dmitry; Schneider, Guido
2017
Justification of modulation equations for hyperbolic systems via normal forms. Zbl 0890.35082
Schneider, Guido
1998
Justification of the nonlinear Schrödinger equation in spatially periodic media. Zbl 1109.35104
Busch, Kurt; Schneider, Guido; Tkeshelashvili, Lasha; Uecker, Hannes
2006
Nonlinear diffusive stability of spatially periodic solutions – abstract theorem and higher space dimensions –. Zbl 0907.35015
Schneider, Guido
1998
Diffusive mixing of periodic wave trains in reaction-diffusion systems. Zbl 1298.35108
Sandstede, Björn; Scheel, Arnd; Schneider, Guido; Uecker, Hannes
2012
Kawahara dynamics in dispersive media. Zbl 0977.35123
Schneider, Guido; Wayne, C. Eugene
2001
Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001
Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian
2011
A new estimate for the Ginzburg-Landau approximation on the real axis. Zbl 0803.35139
Schneider, G.
1994
KP description of unidirectional long waves. The model case. Zbl 1015.76015
Gallay, Thierry; Schneider, Guido
2001
Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. Zbl 1186.35207
Pelinovsky, Dmitry; Schneider, Guido
2010
Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178
Schneider, Guido; Wayne, C. Eugene
2011
Nonlinear stability of Taylor vortices in infinite cylinders. Zbl 0916.76022
Schneider, Guido
1998
The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions. Zbl 1344.35138
Schneider, Guido; Sunny, Danish Ali; Zimmermann, Dominik
2015
Nonlinear PDEs. A dynamical systems approach. Zbl 1402.35001
Schneider, Guido; Uecker, Hannes
2017
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders. Zbl 0922.35015
Hărağuş-Courcelle, Mariana; Schneider, Guido
1999
Global existence results for pattern forming processes in infinite cylindrical domains – applications to 3D Navier-Stokes problems. Zbl 0933.35025
Schneider, Guido
1999
Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. Zbl 1334.35313
Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene
2016
Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Zbl 1162.47059
Pelinovsky, Dmitry; Schneider, Guido; MacKay, Robert S.
2008
Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model. Zbl 1194.35362
Düll, Wolf-Patrick; Schneider, Guido
2006
Long-time persistence of Korteweg-de Vries solitons as transient dynamics in a model of inclined film flow. Zbl 1174.35102
Pego, Robert L.; Schneider, Guido; Uecker, Hannes
2007
Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. Zbl 1248.35182
Chirilus-Bruckner, Martina; Chong, Christopher; Prill, Oskar; Schneider, Guido
2012
Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Zbl 0988.35158
Schneider, Guido; Uecker, Hannes
2001
Validity of the NLS approximation for periodic quantum graphs. Zbl 1367.35156
Gilg, Steffen; Pelinovsky, Dmitry; Schneider, Guido
2016
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Zbl 1132.41344
Pelinovsky, Dmitry; Schneider, Guido
2007
Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. Zbl 1177.35216
Dohnal, Tomáš; Pelinovsky, Dmitry; Schneider, Guido
2009
Rigorous justification of the short-pulse equation. Zbl 1268.35089
Pelinovsky, Dmitry; Schneider, Guido
2013
Comparison of inertial manifolds and application to modulated systems. Zbl 0957.35025
Mielke, A.; Schneider, G.; Ziegra, A.
2000
The validity of generalized Ginzburg-Landau equations. Zbl 0874.35050
Schneider, Guido
1996
Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations. Zbl 0803.35140
Schneider, Guido
1994
The long wave limit for a Boussinesq equation. Zbl 0911.35105
Schneider, Guido
1998
Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation. Zbl 0940.35179
Schneider, Guido
1998
Justification of the Ginzburg-Landau approximation in case of marginally stable long waves. Zbl 1209.35010
Häcker, Tobias; Schneider, Guido; Zimmermann, Dominik
2011
The stochastic Landau equation as an amplitude equation. Zbl 1004.60074
Blömker, D.; Maier-Paape, S.; Schneider, G.
2001
Analyticity of Ginzburg-Landau modes. Zbl 0832.35021
Schneider, Guido
1995
Hopf bifurcation in spatially extended reaction-diffusion systems. Zbl 0899.58048
Schneider, G.
1998
Modulating pulse solutions for quasilinear wave equations. Zbl 1078.35074
Groves, Mark D.; Schneider, Guido
2005
Non-linear stability of modulated fronts for the Swift-Hohenberg equation. Zbl 0994.35057
Eckmann, J.-P.; Schneider, G.
2002
Phase dynamics in the real Ginzburg-Landau equation. Zbl 1057.35064
Melbourne, Ian; Schneider, Guido
2004
Justification of the Ginzburg-Landau approximation for an instability as it appears for Marangoni convection. Zbl 1285.35114
Schneider, Guido; Zimmermann, Dominik
2013
Validity of Whitham’s equations for the modulation of periodic traveling waves in the NLS equation. Zbl 1179.35305
Düll, Wolf-Patrick; Schneider, Guido
2009
On the justification of the Ginzburg-Landau approximation. Zbl 0836.35147
Bollerman, P.; van Harten, A.; Schneider, G.
1995
Modulating pulse solutions for a class of nonlinear wave equations. Zbl 0981.35041
Groves, M. D.; Schneider, G.
2001
Breather solutions in periodic media. Zbl 1223.35234
Blank, Carsten; Chirilus-Bruckner, Martina; Lescarret, Vincent; Schneider, Guido
2011
Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. Zbl 1041.35074
Schneider, Guido; Uecker, Hannes
2003
Hopf bifurcation and exchange of stability in diffusive media. Zbl 1064.35021
Brand, Thomas; Kunze, Markus; Schneider, Guido; Seelbach, Thorsten
2004
Bounds for the nonlinear Schrödinger approximation of the Fermi-Pasta-Ulam system. Zbl 1194.35427
Schneider, Guido
2010
Justification of the NLS approximation for the KdV equation using the Miura transformation. Zbl 1417.37251
Schneider, Guido
2011
Stable transport of information near essentially unstable localized structures. Zbl 1055.35021
Gallay, Thierry; Schneider, Guido; Uecker, Hannes
2004
The amplitude equations for the first instability of electro-convection in nematic liquid crystals in the case of two unbounded space directions. Zbl 1116.76030
Schneider, Guido; Uecker, Hannes
2007
On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Zbl 1252.35247
Chong, Christopher; Pelinovsky, Dmitry E.; Schneider, Guido
2012
Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation. Zbl 0856.35060
Mielke, Alexander; Schneider, Guido
1996
A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in $$\mathbb R^{3}$$. Zbl 1153.37389
Melcher, Andreas; Schneider, Guido; Uecker, Hannes
2008
Stability and diffusive dynamics on extended domains. Zbl 1004.35018
Mielke, Alexander; Schneider, Guido; Uecker, Hannes
2001
Nonlinear stability of bifurcating front solutions for the Taylor-Couette problem. Zbl 0967.35109
Eckmann, J.-P.; Schneider, G.
2000
Phase dynamics in the complex Ginzburg-Landau equation. Zbl 1059.35139
Melbourne, Ian; Schneider, Guido
2004
Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401
Schneider, Guido; Wayne, C. Eugene
2003
On the validity of 2D surface water wave models. Zbl 1096.76504
Schneider, Guido; Wayne, C. Eugene
2002
Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an unbounded domain. Zbl 0929.76043
Schneider, G.
1999
Justification of mean-field coupled modulation equations. Zbl 0880.35108
Schneider, Guido
1997
On the interaction of NLS-described modulating pulses with different carrier waves. Zbl 1149.35392
Chirilus-Bruckner, Martina; Schneider, Guido; Uecker, Hannes
2007
Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves. Zbl 1159.35066
Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido; Uecker, Hannes
2008
NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms. Zbl 1311.35164
Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido
2015
Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation. Zbl 1315.35185
Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido
2014
Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity. Zbl 1280.35133
Chong, Christopher; Schneider, Guido
2013
Some characterizations of the Taylor-Couette attractor. Zbl 1012.35011
Schneider, Guido
1999
Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales. Zbl 1160.35052
Groves, M. D.; Schneider, G.
2008
From the Klein-Gordon-Zakharov system to the Klein-Gordon equation. Zbl 1352.35072
Daub, Markus; Schneider, Guido; Schratz, Katharina
2016
Justification of the equations for the resonant four wave interaction. Zbl 1100.76013
Schneider, Guido; Zink, Oliver
2005
A waiting time phenomenon in pattern forming systems. Zbl 1190.35029
Düll, Wolf-Patrick; Schneider, Guido
2009
The mathematics of light pulses in dispersive media. Zbl 1204.35002
Schneider, Guido; Uecker, Hannes
2007
Detection of standing pulses in periodic media by pulse interaction. Zbl 1259.78030
Chirilus-Bruckner, Martina; Schneider, Guido
2012
Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum. Zbl 1063.35029
Kunze, M.; Schneider, G.
2004
Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves. Zbl 1360.76061
Schneider, Guido
2016
Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times. Zbl 1058.76065
Schneider, Guido; Uecker, Hannes
2003
Modulation equation and SPDEs on unbounded domains. Zbl 1435.35292
Bianchi, Luigi Amedeo; Blömker, Dirk; Schneider, Guido
2019
Corrigendum: the long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1236.76016
Schneider, Guido; Wayne, C. Eugene
2012
Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms. Zbl 1236.35122
Häcker, Tobias; Schneider, Guido; Uecker, Hannes
2012
Interaction of modulated pulses in nonlinear oscillator chains. Zbl 1228.34026
Schneider, Guido; Uecker, Hannes; Wand, Michael
2011
Aproximation and attractivity properties of the degenerated Ginzburg-Landau equation. Zbl 1117.35033
Bitzer, Jochen; Schneider, Guido
2007
Exponential averaging for traveling wave solutions in rapidly varying periodic media. Zbl 1206.35146
Matthies, Karsten; Schneider, Guido; Uecker, Hannes
2007
The validity of the KdV approximation in case of resonances arising from periodic media. Zbl 1241.35175
Chong, Christopher; Schneider, Guido
2011
Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide. Zbl 1253.35173
Lescarret, Vincent; Schneider, Guido
2012
Attractivity of the Ginzburg-Landau mode distribution for a pattern forming system with marginally stable long modes. Zbl 1341.35152
Düll, Wolf-Patrick; Kashani, Kourosh Sanei; Schneider, Guido; Zimmermann, Dominik
2016
Moving gap solitons in periodic potentials. Zbl 1156.35465
Pelinovsky, Dmitry; Schneider, Guido
2008
Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media. Zbl 1262.35169
Lescarret, Vincent; Blank, Carsten; Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido
2009
A proof of validity for multiphase Whitham modulation theory. Zbl 1472.35332
Bridges, Thomas J.; Kostianko, Anna; Schneider, Guido
2020
On the dynamics of the mean-field polaron in the high-frequency limit. Zbl 1436.35289
Griesemer, Marcel; Schmid, Jochen; Schneider, Guido
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 1333.35251
Düll, Wolf-Patrick; Hermann, Alina; Schneider, Guido; Zimmermann, Dominik
2016
Nonlinear stability at the Eckhaus boundary. Zbl 1454.35361
Guillod, Julien; Schneider, Guido; Wittwer, Peter; Zimmermann, Dominik
2018
A proof of validity for multiphase Whitham modulation theory. Zbl 1472.35332
Bridges, Thomas J.; Kostianko, Anna; Schneider, Guido
2020
Global existence and decay in nonlinearly coupled reaction-diffusion-advection equations with different velocities. Zbl 1435.35198
de Rijk, Björn; Schneider, Guido
2020
The monoatomic FPU system as a limit of a diatomic FPU system. Zbl 1442.35456
Pelinovsky, Dmitry E.; Schneider, Guido
2020
Effective slow dynamics models for a class of dispersive systems. Zbl 1452.35014
Baumstark, Simon; Schneider, Guido; Schratz, Katharina; Zimmermann, Dominik
2020
Modulation equation and SPDEs on unbounded domains. Zbl 1435.35292
Bianchi, Luigi Amedeo; Blömker, Dirk; Schneider, Guido
2019
A model for the periodic water wave problem and its long wave amplitude equations. Zbl 1442.35322
Bauer, Roman; Cummings, Patrick; Schneider, Guido
2019
The Korteweg-de Vries, Burgers and Whitham limits for a spatially periodic Boussinesq model. Zbl 1421.35319
Bauer, Roman; Düll, Wolf-Patrick; Schneider, Guido
2019
Nonlinear stability at the Eckhaus boundary. Zbl 1454.35361
Guillod, Julien; Schneider, Guido; Wittwer, Peter; Zimmermann, Dominik
2018
Bifurcations of standing localized waves on periodic graphs. Zbl 1387.35556
Pelinovsky, Dmitry; Schneider, Guido
2017
Nonlinear PDEs. A dynamical systems approach. Zbl 1402.35001
Schneider, Guido; Uecker, Hannes
2017
On the dynamics of the mean-field polaron in the high-frequency limit. Zbl 1436.35289
Griesemer, Marcel; Schmid, Jochen; Schneider, Guido
2017
Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. Zbl 1334.35313
Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene
2016
Validity of the NLS approximation for periodic quantum graphs. Zbl 1367.35156
Gilg, Steffen; Pelinovsky, Dmitry; Schneider, Guido
2016
From the Klein-Gordon-Zakharov system to the Klein-Gordon equation. Zbl 1352.35072
Daub, Markus; Schneider, Guido; Schratz, Katharina
2016
Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves. Zbl 1360.76061
Schneider, Guido
2016
Attractivity of the Ginzburg-Landau mode distribution for a pattern forming system with marginally stable long modes. Zbl 1341.35152
Düll, Wolf-Patrick; Kashani, Kourosh Sanei; Schneider, Guido; Zimmermann, Dominik
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 1333.35251
Düll, Wolf-Patrick; Hermann, Alina; Schneider, Guido; Zimmermann, Dominik
2016
The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions. Zbl 1344.35138
Schneider, Guido; Sunny, Danish Ali; Zimmermann, Dominik
2015
NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms. Zbl 1311.35164
Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido
2015
Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation. Zbl 1315.35185
Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido
2014
Justification of leading order quasicontinuum approximations of strongly nonlinear lattices. Zbl 1307.35256
Chong, Christopher; Kevrekidis, P. G.; Schneider, Guido
2014
Rigorous justification of the short-pulse equation. Zbl 1268.35089
Pelinovsky, Dmitry; Schneider, Guido
2013
Justification of the Ginzburg-Landau approximation for an instability as it appears for Marangoni convection. Zbl 1285.35114
Schneider, Guido; Zimmermann, Dominik
2013
Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity. Zbl 1280.35133
Chong, Christopher; Schneider, Guido
2013
Diffusive mixing of periodic wave trains in reaction-diffusion systems. Zbl 1298.35108
Sandstede, Björn; Scheel, Arnd; Schneider, Guido; Uecker, Hannes
2012
Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. Zbl 1248.35182
Chirilus-Bruckner, Martina; Chong, Christopher; Prill, Oskar; Schneider, Guido
2012
On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Zbl 1252.35247
Chong, Christopher; Pelinovsky, Dmitry E.; Schneider, Guido
2012
Detection of standing pulses in periodic media by pulse interaction. Zbl 1259.78030
Chirilus-Bruckner, Martina; Schneider, Guido
2012
Corrigendum: the long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1236.76016
Schneider, Guido; Wayne, C. Eugene
2012
Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms. Zbl 1236.35122
Häcker, Tobias; Schneider, Guido; Uecker, Hannes
2012
Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide. Zbl 1253.35173
Lescarret, Vincent; Schneider, Guido
2012
Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001
Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian
2011
Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178
Schneider, Guido; Wayne, C. Eugene
2011
Justification of the Ginzburg-Landau approximation in case of marginally stable long waves. Zbl 1209.35010
Häcker, Tobias; Schneider, Guido; Zimmermann, Dominik
2011
Breather solutions in periodic media. Zbl 1223.35234
Blank, Carsten; Chirilus-Bruckner, Martina; Lescarret, Vincent; Schneider, Guido
2011
Justification of the NLS approximation for the KdV equation using the Miura transformation. Zbl 1417.37251
Schneider, Guido
2011
Interaction of modulated pulses in nonlinear oscillator chains. Zbl 1228.34026
Schneider, Guido; Uecker, Hannes; Wand, Michael
2011
The validity of the KdV approximation in case of resonances arising from periodic media. Zbl 1241.35175
Chong, Christopher; Schneider, Guido
2011
Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. Zbl 1186.35207
Pelinovsky, Dmitry; Schneider, Guido
2010
Bounds for the nonlinear Schrödinger approximation of the Fermi-Pasta-Ulam system. Zbl 1194.35427
Schneider, Guido
2010
The dynamics of modulated wave trains. Zbl 1179.35005
Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido
2009
Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. Zbl 1177.35216
Dohnal, Tomáš; Pelinovsky, Dmitry; Schneider, Guido
2009
Validity of Whitham’s equations for the modulation of periodic traveling waves in the NLS equation. Zbl 1179.35305
Düll, Wolf-Patrick; Schneider, Guido
2009
A waiting time phenomenon in pattern forming systems. Zbl 1190.35029
Düll, Wolf-Patrick; Schneider, Guido
2009
Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media. Zbl 1262.35169
Lescarret, Vincent; Blank, Carsten; Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido
2009
Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Zbl 1162.47059
Pelinovsky, Dmitry; Schneider, Guido; MacKay, Robert S.
2008
A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in $$\mathbb R^{3}$$. Zbl 1153.37389
Melcher, Andreas; Schneider, Guido; Uecker, Hannes
2008
Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves. Zbl 1159.35066
Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido; Uecker, Hannes
2008
Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales. Zbl 1160.35052
Groves, M. D.; Schneider, G.
2008
Moving gap solitons in periodic potentials. Zbl 1156.35465
Pelinovsky, Dmitry; Schneider, Guido
2008
Long-time persistence of Korteweg-de Vries solitons as transient dynamics in a model of inclined film flow. Zbl 1174.35102
Pego, Robert L.; Schneider, Guido; Uecker, Hannes
2007
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Zbl 1132.41344
Pelinovsky, Dmitry; Schneider, Guido
2007
The amplitude equations for the first instability of electro-convection in nematic liquid crystals in the case of two unbounded space directions. Zbl 1116.76030
Schneider, Guido; Uecker, Hannes
2007
On the interaction of NLS-described modulating pulses with different carrier waves. Zbl 1149.35392
Chirilus-Bruckner, Martina; Schneider, Guido; Uecker, Hannes
2007
The mathematics of light pulses in dispersive media. Zbl 1204.35002
Schneider, Guido; Uecker, Hannes
2007
Aproximation and attractivity properties of the degenerated Ginzburg-Landau equation. Zbl 1117.35033
Bitzer, Jochen; Schneider, Guido
2007
Exponential averaging for traveling wave solutions in rapidly varying periodic media. Zbl 1206.35146
Matthies, Karsten; Schneider, Guido; Uecker, Hannes
2007
Justification of the nonlinear Schrödinger equation in spatially periodic media. Zbl 1109.35104
Busch, Kurt; Schneider, Guido; Tkeshelashvili, Lasha; Uecker, Hannes
2006
Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model. Zbl 1194.35362
Düll, Wolf-Patrick; Schneider, Guido
2006
Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances. Zbl 1075.35080
Schneider, Guido
2005
Modulating pulse solutions for quasilinear wave equations. Zbl 1078.35074
Groves, Mark D.; Schneider, Guido
2005
Justification of the equations for the resonant four wave interaction. Zbl 1100.76013
Schneider, Guido; Zink, Oliver
2005
Local in time and space nonlinear stability of pulses in an unstable medium. Zbl 1106.76032
Schneider, Guido; Pego, Robert L.; Uecker, Hannes
2005
Estimates for the KdV-limit of the Camassa-Holm equation. Zbl 1084.35074
Kunze, Markus; Schneider, Guido
2005
Phase dynamics in the real Ginzburg-Landau equation. Zbl 1057.35064
Melbourne, Ian; Schneider, Guido
2004
Hopf bifurcation and exchange of stability in diffusive media. Zbl 1064.35021
Brand, Thomas; Kunze, Markus; Schneider, Guido; Seelbach, Thorsten
2004
Stable transport of information near essentially unstable localized structures. Zbl 1055.35021
Gallay, Thierry; Schneider, Guido; Uecker, Hannes
2004
Phase dynamics in the complex Ginzburg-Landau equation. Zbl 1059.35139
Melbourne, Ian; Schneider, Guido
2004
Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum. Zbl 1063.35029
Kunze, M.; Schneider, G.
2004
Validity of the Ginzburg-Landau approximation in pattern forming systems with time periodic forcing. Zbl 1093.35035
Breindl, Norbert; Schneider, Guido; Uecker, Hannes
2004
Propagation of hexagonal patterns near onset. Zbl 1044.37049
Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido
2003
Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. Zbl 1041.35074
Schneider, Guido; Uecker, Hannes
2003
Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401
Schneider, Guido; Wayne, C. Eugene
2003
Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times. Zbl 1058.76065
Schneider, Guido; Uecker, Hannes
2003
The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006
Schneider, Guido; Wayne, C. Eugene
2002
Non-linear stability of modulated fronts for the Swift-Hohenberg equation. Zbl 0994.35057
Eckmann, J.-P.; Schneider, G.
2002
On the validity of 2D surface water wave models. Zbl 1096.76504
Schneider, Guido; Wayne, C. Eugene
2002
Kawahara dynamics in dispersive media. Zbl 0977.35123
Schneider, Guido; Wayne, C. Eugene
2001
KP description of unidirectional long waves. The model case. Zbl 1015.76015
Gallay, Thierry; Schneider, Guido
2001
Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Zbl 0988.35158
Schneider, Guido; Uecker, Hannes
2001
The stochastic Landau equation as an amplitude equation. Zbl 1004.60074
Blömker, D.; Maier-Paape, S.; Schneider, G.
2001
Modulating pulse solutions for a class of nonlinear wave equations. Zbl 0981.35041
Groves, M. D.; Schneider, G.
2001
Stability and diffusive dynamics on extended domains. Zbl 1004.35018
Mielke, Alexander; Schneider, Guido; Uecker, Hannes
2001
Bifurcation analysis for a spatially extended random walk system in mathematical biology. Zbl 1084.35545
Schneider, Guido; Müller, Johannes
2001
The long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1034.76011
Schneider, Guido; Wayne, C. Eugene
2000
Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model. Zbl 0970.35126
Schneider, Guido; Wayne, C. Eugene
2000
Comparison of inertial manifolds and application to modulated systems. Zbl 0957.35025
Mielke, A.; Schneider, G.; Ziegra, A.
2000
Nonlinear stability of bifurcating front solutions for the Taylor-Couette problem. Zbl 0967.35109
Eckmann, J.-P.; Schneider, G.
2000
Existence and stability of modulating pulse-solutions in a phenomenological model of nonlinear optics. Zbl 0954.35148
Schneider, Guido
2000
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders. Zbl 0922.35015
Hărağuş-Courcelle, Mariana; Schneider, Guido
1999
Global existence results for pattern forming processes in infinite cylindrical domains – applications to 3D Navier-Stokes problems. Zbl 0933.35025
Schneider, Guido
1999
Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an unbounded domain. Zbl 0929.76043
Schneider, G.
1999
Some characterizations of the Taylor-Couette attractor. Zbl 1012.35011
Schneider, Guido
1999
Justification of modulation equations for hyperbolic systems via normal forms. Zbl 0890.35082
Schneider, Guido
1998
Nonlinear diffusive stability of spatially periodic solutions – abstract theorem and higher space dimensions –. Zbl 0907.35015
Schneider, Guido
1998
Nonlinear stability of Taylor vortices in infinite cylinders. Zbl 0916.76022
Schneider, Guido
1998
The long wave limit for a Boussinesq equation. Zbl 0911.35105
Schneider, Guido
1998
Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation. Zbl 0940.35179
Schneider, Guido
1998
Hopf bifurcation in spatially extended reaction-diffusion systems. Zbl 0899.58048
Schneider, G.
1998
Justification of mean-field coupled modulation equations. Zbl 0880.35108
Schneider, Guido
1997
...and 13 more Documents
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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
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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
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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)