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## Wayne, Clarence Eugene

Compute Distance To:
 Author ID: wayne.c-eugene Published as: Wayne, C. E.; Wayne, C. Eugene; Wayne, Clarence Eugene; Wayne, E. External Links: MGP · dblp · GND
 Documents Indexed: 86 Publications since 1983, including 2 Books
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#### Co-Authors

 12 single-authored 10 Eckmann, Jean-Pierre 9 Schneider, Guido 7 Gallay, Thierry 6 Beck, Margaret 5 Craig, Walter 5 Hoffman, Aaron 4 de la Llave, Rafael 2 Banyaga, Augustin 2 Chaudhary, Osman 2 Fröhlich, Jürg Martin 2 Krigman, S. S. 2 Spencer, Thomas C. 2 Uminsky, David T. 1 Barbaro, Alethea B. T. 1 Bardos, Claude Williams 1 Barry, Anna M. 1 Benes, G. Nicholas 1 Bona, Jerry Lloyd 1 Brandenberger, Robert H. 1 Chen, Goong 1 Chirilus-Bruckner, Martina 1 Chueshov, Igor’ Dmitrievich 1 Chung, Yunro 1 Coleman, Matthew P. 1 Cummings, Patrick 1 Cuneo, Noé 1 Curry, James H. 1 Deift, Percy A. 1 Deville, R. E. Lee 1 Düll, Wolf-Patrick 1 Eliasson, L. Hakan 1 Epstein, Henri 1 Goh, Ryan N. 1 Guyenne, Philippe 1 Hall, Glen Richard 1 Jackson, Russell K. 1 Jones, Christoper K. R. T. 1 Josić, Krešimir 1 Kappeler, Thomas 1 Kokarev, Gerasim 1 Krantz, Steven George 1 Kuksin, Sergeĭ B. 1 Levermore, C. David 1 Matthies, Karsten 1 McQuighan, Kelly 1 Nagem, Raymond J. 1 Piatnitski, Andrey L. 1 Pierce, Robert D. 1 Pillet, Claude-Alain 1 Pinto, David J. 1 Popović, Nikola 1 Promislow, Keith Steven 1 Rottschäfer, Vivi 1 Russel, David L. 1 Sandri, Guido v. H. 1 Saut, Jean-Claude 1 Schafer, Thomas 1 Schafer, Toryn L. J. 1 Shirikyan, Armen R. 1 Sulem, Catherine 1 Thomas, Lawrence E. 1 van Baalen, Guillaume 1 Weinstein, Michael I. 1 West, Harry H. 1 Wittwer, Peter 1 Wright, J. Douglas
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#### Serials

 12 Communications in Mathematical Physics 7 Nonlinearity 5 Archive for Rational Mechanics and Analysis 5 SIAM Journal on Applied Dynamical Systems 4 Journal of Mathematical Analysis and Applications 4 Journal of Differential Equations 3 Communications on Pure and Applied Mathematics 3 Journal of Statistical Physics 3 Physica D 3 Notices of the American Mathematical Society 2 Russian Mathematical Surveys 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Mathematical Physics Electronic Journal 1 Journal of Computational Physics 1 Journal of Mathematical Physics 1 Mathematische Zeitschrift 1 Transactions of the American Mathematical Society 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Asymptotic Analysis 1 European Journal of Applied Mathematics 1 Differential and Integral Equations 1 The Journal of Geometric Analysis 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Discrete and Continuous Dynamical Systems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Mathematical Fluid Mechanics 1 Frontiers in Applied Dynamical Systems: Reviews and Tutorials
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#### Fields

 57 Partial differential equations (35-XX) 28 Dynamical systems and ergodic theory (37-XX) 28 Fluid mechanics (76-XX) 9 Ordinary differential equations (34-XX) 8 Mechanics of particles and systems (70-XX) 7 Statistical mechanics, structure of matter (82-XX) 4 Probability theory and stochastic processes (60-XX) 4 Optics, electromagnetic theory (78-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of deformable solids (74-XX) 2 History and biography (01-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

72 Publications have been cited 1,404 times in 1,003 Documents Cited by Year
Newton’s method and periodic solutions of nonlinear wave equations. Zbl 0794.35104
Craig, Walter; Wayne, C. Eugene
1993
Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Zbl 0708.35087
Wayne, C. Eugene
1990
Propagation of ultra-short optical pulses in cubic nonlinear media. Zbl 1054.81554
Schäfer, T.; Wayne, C. E.
2004
Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on $$\mathbb R^2$$. Zbl 1042.37058
Gallay, Thierry; Wayne, C. Eugene
2002
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
Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations. Zbl 0890.35016
Pillet, Claude-Alain; Wayne, C. Eugene
1997
Global stability of vortex solutions of the two-dimensional Navier-Stokes equation. Zbl 1139.35084
Gallay, Thierry; Wayne, C. Eugene
2005
Ultra-short pulses in linear and nonlinear media. Zbl 1125.35412
Chung, Y.; Jones, C. K. R. T.; Schäfer, T.; Wayne, C. E.
2005
Localization in disordered, nonlinear dynamical systems. Zbl 0629.60105
Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene
1986
The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006
Schneider, Guido; Wayne, C. Eugene
2002
Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier-Stokes equations. Zbl 1296.35114
Beck, Margaret; Wayne, C. Eugene
2013
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
Propagating fronts and the center manifold theorem. Zbl 0790.34045
Eckmann, J.-P.; Wayne, C. E.
1991
Long-time asymptotics of the Navier-Stokes and vorticity equations on $${\mathbb R}^ 3$$. Recent developments in the mathematical theory of water waves (Oberwolfach, 2001). Zbl 1048.35055
Gallay, Thierry; Wayne, C. Eugene
2002
On Irwin’s proof of the pseudostable manifold theorem. Zbl 0843.58100
de la Llave, Rafael; Wayne, C. Eugene
1995
Invariant manifolds for parabolic partial differential equations on unbounded domains. Zbl 0882.35061
Wayne, C. Eugene
1997
Cohomology equations near hyperbolic points and geometric versions of Sternberg linearization theorem. Zbl 0918.53016
Banyaga, A.; de la Llave, R.; Wayne, C. E.
1996
Kawahara dynamics in dispersive media. Zbl 0977.35123
Schneider, Guido; Wayne, C. Eugene
2001
Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178
Schneider, Guido; Wayne, C. Eugene
2011
Analysis, designs, and behaviour of dissipative joints for coupled beams. Zbl 0685.73046
Chen, G.; Krantz, S. G.; Russel, D. L.; Wayne, C. E.; West, H. H.; Coleman, M. P.
1989
Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349
de la Llave, R.; Wayne, C. E.
2004
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
The nonlinear stability of front solutions for parabolic partial differential equations. Zbl 0817.35036
Eckmann, Jean-Pierre; Wayne, C. Eugene
1994
Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice. Zbl 1153.82323
Hoffman, A.; Wayne, C. E.
2008
On the validity of mean-field amplitude equations for counterpropagating wavetrains. Zbl 0833.35128
Pierce, R. D.; Wayne, C. E.
1995
Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model. Zbl 1172.35066
Hoffman, Aaron; Wayne, C. E.
2009
Mathematical aspects of surface water waves. Zbl 1203.76023
Craig, W.; Wayne, C. E.
2007
Existence and stability of traveling pulses in a continuous neuronal network. Zbl 1091.45004
Pinto, David J.; Jackson, Russell K.; Wayne, C. Eugene
2005
Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation. Zbl 0912.35140
Eckmann, Jean-Pierre; Wayne, C. Eugene; Wittwer, Peter
1997
Higher-order asymptotics of decaying solutions of some nonlinear, dispersive, dissipative wave equations. Zbl 0837.35130
Bona, J. L.; Promislow, K. S.; Wayne, C. E.
1995
Existence and stability of asymmetric Burgers vortices. Zbl 1119.76012
Gallay, Thierry; Wayne, C. Eugene
2007
Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1227.35061
Beck, Margaret; Wayne, C. Eugene
2011
Existence and stability of traveling fronts in the extended Fisher-Kolmogorov equation. Zbl 1109.35361
Rottschäfer, V.; Wayne, C. E.
2001
The KAM theory of systems with short range interactions. I. Zbl 0585.58023
Wayne, C. Eugene
1984
Relative equilibria of the $$(1+N)$$-vortex problem. Zbl 1329.76047
Barry, Anna M.; Hall, Glen R.; Wayne, C. Eugene
2012
Three-dimensional stability of Burgers vortices: the low Reynolds number case. Zbl 1091.35080
Gallay, Thierry; Wayne, C. Eugene
2006
Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401
Schneider, Guido; Wayne, C. Eugene
2003
Liapunov spectra for infinite chains of nonlinear oscillators. Zbl 1084.37500
Eckmann, Jean-Pierre; Wayne, C. Eugene
1988
A simple proof of the stability of solitary waves in the Fermi-Pasta-Ulam model near the KdV limit. Zbl 1275.37035
Hoffman, A.; Wayne, C. Eugene
2012
Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1201.35044
Beck, Margaret; Wayne, C. Eugene
2009
Generalized Helmholtz-Kirchhoff model for two-dimensional distributed vortex motion. Zbl 1408.76205
Nagem, Raymond; Sandri, Guido; Uminsky, David; Wayne, C. Eugene
2009
Boundary controllability of Maxwell’s equations with nonzero conductivity inside a cube. I. Spectral controllability. Zbl 1154.93317
Krigman, S. S.; Wayne, C. E.
2007
On the validity of 2D surface water wave models. Zbl 1096.76504
Schneider, Guido; Wayne, C. Eugene
2002
Higher-order modulation equations for a Boussinesq equation. Zbl 1088.76007
Wayne, C. Eugene; Wright, J. Douglas
2002
Normal forms for parabolic partial differential equations. Zbl 0791.35057
Eckmann, J.-P.; Epstein, H.; Wayne, C. E.
1993
Cohomology equations and commutators of germs of contact diffeomorphisms. Zbl 0671.58031
Banyaga, Augustin; de la Llave, Rafael; Wayne, C. Eugene
1989
Bounds on the trajectories of a system of weakly coupled rotators. Zbl 0615.70013
Wayne, C. Eugene
1986
On the stability of dense point spectrum for self-adjoint operators. Zbl 0608.47018
Thomas, Lawrence E.; Wayne, C. Eugene
1986
On the elimination of non-resonance harmonics. Zbl 0596.58021
Wayne, C. Eugene
1986
A multi-moment vortex method for 2D viscous fluids. Zbl 1408.76210
Uminsky, David; Wayne, C. Eugene; Barbaro, Alethea
2012
Long-time asymptotics of the Navier-Stokes equation in $$\mathbb R^{2}$$ and $$\mathbb R^{3}$$. Zbl 1094.35089
Gallay, Thierry; Wayne, C. Eugene
2006
Periodic solutions of nonlinear partial differential equations. Zbl 0912.35016
Wayne, C. Eugene
1997
An introduction to KAM theory. Zbl 0844.58037
Wayne, C. Eugene
1996
Asymptotic stability of the Toda $$m$$-soliton. Zbl 1226.82006
Benes, G. N.; Hoffman, A.; Wayne, C. E.
2012
Vortices and two-dimensional fluid motion. Zbl 1372.76002
Wayne, C. Eugene
2011
Boundary controllability of Maxwell’s equations with nonzero conductivity inside a cube. II. Lack of exact controllability and controllability for very smooth solutions. Zbl 1154.93316
Krigman, S. S.; Wayne, C. E.
2007
Wave pinning in strips. Zbl 1119.35027
Matthies, Karsten; Wayne, C. E.
2006
Phase slips and the Eckhaus instability. Zbl 0846.35032
Eckmann, J.-P.; Gallay, Th.; Wayne, C. E.
1995
Nonlinear waves and the $$1:1:2$$ resonance. Zbl 0849.35133
Craig, Walter; Wayne, C. Eugene
1994
Modified energy functionals and the NLS approximation. Zbl 1375.35406
Wayne, C. Eugene; Cummings, Patrick
2017
Orbital stability of localized structures via Bäcklund transformations. Zbl 1289.35225
Hoffman, Aaron; Wayne, C. Eugene
2013
Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws. Zbl 1145.35081
Beck, Margaret; Wayne, C. Eugene
2008
Dynamics of a ring of diffusively coupled Lorenz oscillators. Zbl 0996.37037
Josić, Krešimir; Wayne, C. Eugene
2000
The largest Lyapunov exponent for random matrices and directed polymers in a random environment. Zbl 0673.60066
Eckmann, J.-P.; Wayne, C. E.
1989
The KAM theory of systems with short range interactions. II. Zbl 0595.58022
Wayne, C. Eugene
1984
Vortices in stably-stratified rapidly rotating Boussinesq convection. Zbl 1414.35167
Goh, Ryan; Wayne, C. Eugene
2019
Energy dissipation in Hamiltonian chains of rotators. Zbl 1456.37065
Cuneo, Noé; Eckmann, Jean-Pierre; Wayne, C. Eugene
2017
An explanation of metastability in the viscous Burgers equation with periodic boundary conditions via a spectral analysis. Zbl 1361.35081
McQuighan, Kelly; Wayne, C. Eugene
2016
Analysis of enhanced diffusion in Taylor dispersion via a model problem. Zbl 1331.35270
Beck, Margaret; Chaudhary, Osman; Wayne, C. Eugene
2015
Dynamics of partial differential equations. Zbl 1331.35006
Wayne, C. Eugene; Weinstein, Michael I.
2015
Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem. Zbl 1325.34021
Chirilus-Bruckner, Martina; Wayne, Clarence Eugene
2015
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
Vortices in stably-stratified rapidly rotating Boussinesq convection. Zbl 1414.35167
Goh, Ryan; Wayne, C. Eugene
2019
Modified energy functionals and the NLS approximation. Zbl 1375.35406
Wayne, C. Eugene; Cummings, Patrick
2017
Energy dissipation in Hamiltonian chains of rotators. Zbl 1456.37065
Cuneo, Noé; Eckmann, Jean-Pierre; Wayne, C. Eugene
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
An explanation of metastability in the viscous Burgers equation with periodic boundary conditions via a spectral analysis. Zbl 1361.35081
McQuighan, Kelly; Wayne, C. Eugene
2016
Analysis of enhanced diffusion in Taylor dispersion via a model problem. Zbl 1331.35270
Beck, Margaret; Chaudhary, Osman; Wayne, C. Eugene
2015
Dynamics of partial differential equations. Zbl 1331.35006
Wayne, C. Eugene; Weinstein, Michael I.
2015
Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem. Zbl 1325.34021
Chirilus-Bruckner, Martina; Wayne, Clarence Eugene
2015
Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier-Stokes equations. Zbl 1296.35114
Beck, Margaret; Wayne, C. Eugene
2013
Orbital stability of localized structures via Bäcklund transformations. Zbl 1289.35225
Hoffman, Aaron; Wayne, C. Eugene
2013
Relative equilibria of the $$(1+N)$$-vortex problem. Zbl 1329.76047
Barry, Anna M.; Hall, Glen R.; Wayne, C. Eugene
2012
A simple proof of the stability of solitary waves in the Fermi-Pasta-Ulam model near the KdV limit. Zbl 1275.37035
Hoffman, A.; Wayne, C. Eugene
2012
A multi-moment vortex method for 2D viscous fluids. Zbl 1408.76210
Uminsky, David; Wayne, C. Eugene; Barbaro, Alethea
2012
Asymptotic stability of the Toda $$m$$-soliton. Zbl 1226.82006
Benes, G. N.; Hoffman, A.; Wayne, C. E.
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
Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178
Schneider, Guido; Wayne, C. Eugene
2011
Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1227.35061
Beck, Margaret; Wayne, C. Eugene
2011
Vortices and two-dimensional fluid motion. Zbl 1372.76002
Wayne, C. Eugene
2011
Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model. Zbl 1172.35066
Hoffman, Aaron; Wayne, C. E.
2009
Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1201.35044
Beck, Margaret; Wayne, C. Eugene
2009
Generalized Helmholtz-Kirchhoff model for two-dimensional distributed vortex motion. Zbl 1408.76205
Nagem, Raymond; Sandri, Guido; Uminsky, David; Wayne, C. Eugene
2009
Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice. Zbl 1153.82323
Hoffman, A.; Wayne, C. E.
2008
Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws. Zbl 1145.35081
Beck, Margaret; Wayne, C. Eugene
2008
Mathematical aspects of surface water waves. Zbl 1203.76023
Craig, W.; Wayne, C. E.
2007
Existence and stability of asymmetric Burgers vortices. Zbl 1119.76012
Gallay, Thierry; Wayne, C. Eugene
2007
Boundary controllability of Maxwell’s equations with nonzero conductivity inside a cube. I. Spectral controllability. Zbl 1154.93317
Krigman, S. S.; Wayne, C. E.
2007
Boundary controllability of Maxwell’s equations with nonzero conductivity inside a cube. II. Lack of exact controllability and controllability for very smooth solutions. Zbl 1154.93316
Krigman, S. S.; Wayne, C. E.
2007
Three-dimensional stability of Burgers vortices: the low Reynolds number case. Zbl 1091.35080
Gallay, Thierry; Wayne, C. Eugene
2006
Long-time asymptotics of the Navier-Stokes equation in $$\mathbb R^{2}$$ and $$\mathbb R^{3}$$. Zbl 1094.35089
Gallay, Thierry; Wayne, C. Eugene
2006
Wave pinning in strips. Zbl 1119.35027
Matthies, Karsten; Wayne, C. E.
2006
Global stability of vortex solutions of the two-dimensional Navier-Stokes equation. Zbl 1139.35084
Gallay, Thierry; Wayne, C. Eugene
2005
Ultra-short pulses in linear and nonlinear media. Zbl 1125.35412
Chung, Y.; Jones, C. K. R. T.; Schäfer, T.; Wayne, C. E.
2005
Existence and stability of traveling pulses in a continuous neuronal network. Zbl 1091.45004
Pinto, David J.; Jackson, Russell K.; Wayne, C. Eugene
2005
Propagation of ultra-short optical pulses in cubic nonlinear media. Zbl 1054.81554
Schäfer, T.; Wayne, C. E.
2004
Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349
de la Llave, R.; Wayne, C. E.
2004
Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401
Schneider, Guido; Wayne, C. Eugene
2003
Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on $$\mathbb R^2$$. Zbl 1042.37058
Gallay, Thierry; Wayne, C. Eugene
2002
The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006
Schneider, Guido; Wayne, C. Eugene
2002
Long-time asymptotics of the Navier-Stokes and vorticity equations on $${\mathbb R}^ 3$$. Recent developments in the mathematical theory of water waves (Oberwolfach, 2001). Zbl 1048.35055
Gallay, Thierry; Wayne, C. Eugene
2002
On the validity of 2D surface water wave models. Zbl 1096.76504
Schneider, Guido; Wayne, C. Eugene
2002
Higher-order modulation equations for a Boussinesq equation. Zbl 1088.76007
Wayne, C. Eugene; Wright, J. Douglas
2002
Kawahara dynamics in dispersive media. Zbl 0977.35123
Schneider, Guido; Wayne, C. Eugene
2001
Existence and stability of traveling fronts in the extended Fisher-Kolmogorov equation. Zbl 1109.35361
Rottschäfer, V.; Wayne, C. E.
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
Dynamics of a ring of diffusively coupled Lorenz oscillators. Zbl 0996.37037
Josić, Krešimir; Wayne, C. Eugene
2000
Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations. Zbl 0890.35016
Pillet, Claude-Alain; Wayne, C. Eugene
1997
Invariant manifolds for parabolic partial differential equations on unbounded domains. Zbl 0882.35061
Wayne, C. Eugene
1997
Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation. Zbl 0912.35140
Eckmann, Jean-Pierre; Wayne, C. Eugene; Wittwer, Peter
1997
Periodic solutions of nonlinear partial differential equations. Zbl 0912.35016
Wayne, C. Eugene
1997
Cohomology equations near hyperbolic points and geometric versions of Sternberg linearization theorem. Zbl 0918.53016
Banyaga, A.; de la Llave, R.; Wayne, C. E.
1996
An introduction to KAM theory. Zbl 0844.58037
Wayne, C. Eugene
1996
On Irwin’s proof of the pseudostable manifold theorem. Zbl 0843.58100
de la Llave, Rafael; Wayne, C. Eugene
1995
On the validity of mean-field amplitude equations for counterpropagating wavetrains. Zbl 0833.35128
Pierce, R. D.; Wayne, C. E.
1995
Higher-order asymptotics of decaying solutions of some nonlinear, dispersive, dissipative wave equations. Zbl 0837.35130
Bona, J. L.; Promislow, K. S.; Wayne, C. E.
1995
Phase slips and the Eckhaus instability. Zbl 0846.35032
Eckmann, J.-P.; Gallay, Th.; Wayne, C. E.
1995
The nonlinear stability of front solutions for parabolic partial differential equations. Zbl 0817.35036
Eckmann, Jean-Pierre; Wayne, C. Eugene
1994
Nonlinear waves and the $$1:1:2$$ resonance. Zbl 0849.35133
Craig, Walter; Wayne, C. Eugene
1994
Newton’s method and periodic solutions of nonlinear wave equations. Zbl 0794.35104
Craig, Walter; Wayne, C. Eugene
1993
Normal forms for parabolic partial differential equations. Zbl 0791.35057
Eckmann, J.-P.; Epstein, H.; Wayne, C. E.
1993
Propagating fronts and the center manifold theorem. Zbl 0790.34045
Eckmann, J.-P.; Wayne, C. E.
1991
Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Zbl 0708.35087
Wayne, C. Eugene
1990
Analysis, designs, and behaviour of dissipative joints for coupled beams. Zbl 0685.73046
Chen, G.; Krantz, S. G.; Russel, D. L.; Wayne, C. E.; West, H. H.; Coleman, M. P.
1989
Cohomology equations and commutators of germs of contact diffeomorphisms. Zbl 0671.58031
Banyaga, Augustin; de la Llave, Rafael; Wayne, C. Eugene
1989
The largest Lyapunov exponent for random matrices and directed polymers in a random environment. Zbl 0673.60066
Eckmann, J.-P.; Wayne, C. E.
1989
Liapunov spectra for infinite chains of nonlinear oscillators. Zbl 1084.37500
Eckmann, Jean-Pierre; Wayne, C. Eugene
1988
Localization in disordered, nonlinear dynamical systems. Zbl 0629.60105
Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene
1986
Bounds on the trajectories of a system of weakly coupled rotators. Zbl 0615.70013
Wayne, C. Eugene
1986
On the stability of dense point spectrum for self-adjoint operators. Zbl 0608.47018
Thomas, Lawrence E.; Wayne, C. Eugene
1986
On the elimination of non-resonance harmonics. Zbl 0596.58021
Wayne, C. Eugene
1986
The KAM theory of systems with short range interactions. I. Zbl 0585.58023
Wayne, C. Eugene
1984
The KAM theory of systems with short range interactions. II. Zbl 0595.58022
Wayne, C. Eugene
1984
all top 5

#### Cited by 1,143 Authors

 32 Schneider, Guido 28 Wayne, Clarence Eugene 23 Berti, Massimiliano 22 Geng, Jiansheng 21 Procesi, Michela 20 de la Llave, Rafael 19 Bambusi, Dario 18 Gallay, Thierry 15 Düll, Wolf-Patrick 15 Yuan, Xiaoping 13 Ji, Shuguan 13 Pelinovsky, Dmitry Efimovich 12 Bedrossian, Jacob 12 Cuccagna, Scipio 11 Maekawa, Yasunori 11 Xu, Junxiang 10 Bona, Jerry Lloyd 10 Xu, XinDong 9 Bolle, Philippe 9 Coclite, Giuseppe Maria 9 Feng, Baofeng 9 Gao, Meina 9 Si, Jianguo 8 Di Ruvo, Lorenzo 8 Li, Yong 8 Liu, Jianjun 8 Masmoudi, Nader 8 Shi, Yanling 8 You, Jiangong 7 Cong, Hongzi 7 Gentile, Guido 7 Grébert, Benoît 7 Lannes, David 7 Liu, Yue 7 Montalto, Riccardo 7 Qu, Changzheng 7 Stefanov, Atanas G. 7 Uecker, Hannes 6 Biasco, Luca 6 Chirilus-Bruckner, Martina 6 Coti Zelati, Michele 6 Craig, Walter 6 Eckmann, Jean-Pierre 6 Gao, Yixian 6 Kevrekidis, Panayotis G. 6 Matthies, Karsten 6 Ohta, Yasuhiro 6 Pu, Xueke 6 Scheel, Arnd 6 Wang, Wei-Min 5 Beck, Margaret 5 Bourgain, Jean 5 Fontich, Ernest 5 Fu, Ying 5 Germain, Pierre 5 Herrmann, Michael 5 James, Guillaume 5 Kalisch, Henrik 5 Komech, Alexander Ilich 5 Li, Jibin 5 Mi, Lufang 5 Sun, Shuming 5 Zhang, Bingyu 5 Zhang, Weinian 5 Zhang, Wenmeng 5 Zhang, Zhifei 4 Baldi, Pietro 4 Brandolese, Lorenzo 4 Chierchia, Luigi 4 Chong, Christopher 4 Comech, Andrew 4 Corsi, Livia 4 ElBialy, Mohamed Sami 4 Faye, Grégory 4 Feola, Roberto 4 García-Azpeitia, Carlos 4 Guardia, Marcel 4 Guo, Yanfeng 4 Haus, Emanuele 4 Hayashi, Nakao 4 Hoffman, Aaron 4 Holzer, Matt 4 Israwi, Samer 4 Kaloshin, Vadim Yu. 4 Kirr, Eduard 4 Kopylova, Elena A. 4 Liu, Zhihua 4 Lou, Zhaowei 4 Lu, Kening 4 Maeda, Masaya 4 Maruno, Kenichi 4 Naumkin, Pavel Ivanovich 4 Rousset, Frédéric 4 Rui, Jie 4 Strani, Marta 4 Sulem, Catherine 4 Tsai, Tai-Peng 4 Wei, Dongyi 4 Wei, Hui 4 Weinstein, Michael I. ...and 1,043 more Authors
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#### Cited in 200 Serials

 88 Journal of Differential Equations 68 Communications in Mathematical Physics 49 Physica D 41 Archive for Rational Mechanics and Analysis 34 Journal of Mathematical Physics 34 Journal of Dynamics and Differential Equations 29 Journal of Mathematical Analysis and Applications 24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 22 Discrete and Continuous Dynamical Systems 21 Journal of Nonlinear Science 18 Journal of Functional Analysis 16 Communications in Partial Differential Equations 15 Journal of Statistical Physics 14 Applicable Analysis 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 SIAM Journal on Mathematical Analysis 11 Communications on Pure and Applied Mathematics 11 Advances in Mathematics 11 Journal of Mathematical Fluid Mechanics 10 Transactions of the American Mathematical Society 10 SIAM Journal on Applied Dynamical Systems 9 Applied Mathematics and Computation 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Chaos 8 Nonlinearity 8 Discrete and Continuous Dynamical Systems. Series B 7 Mathematical Methods in the Applied Sciences 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Communications in Nonlinear Science and Numerical Simulation 7 Nonlinear Analysis. Real World Applications 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Theoretical and Mathematical Physics 6 Duke Mathematical Journal 6 Inventiones Mathematicae 6 Journal of Computational and Applied Mathematics 6 Memoirs of the American Mathematical Society 6 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Nonlinear Dynamics 6 Regular and Chaotic Dynamics 6 Science China. Mathematics 5 Journal of Fluid Mechanics 5 Mathematische Annalen 5 Mathematische Zeitschrift 5 Quarterly of Applied Mathematics 5 Studies in Applied Mathematics 5 Applied Mathematics Letters 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 NoDEA. Nonlinear Differential Equations and Applications 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 Boundary Value Problems 4 Reviews in Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Systems & Control Letters 4 Acta Applicandae Mathematicae 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Annales de l’Institut Henri Poincaré. Physique Théorique 4 Journal of the European Mathematical Society (JEMS) 4 Journal of Nonlinear Mathematical Physics 4 Communications on Pure and Applied Analysis 4 Journal of Applied Analysis and Computation 4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Letters in Mathematical Physics 3 Wave Motion 3 Journal of Geometry and Physics 3 BIT 3 Mathematics and Computers in Simulation 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Siberian Mathematical Journal 3 Chinese Annals of Mathematics. Series B 3 Geometric and Functional Analysis. GAFA 3 SIAM Journal on Applied Mathematics 3 Calculus of Variations and Partial Differential Equations 3 Journal of Mathematical Sciences (New York) 3 Abstract and Applied Analysis 3 Taiwanese Journal of Mathematics 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Journal of High Energy Physics 3 Annales Henri Poincaré 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Frontiers of Mathematics in China 3 Discrete and Continuous Dynamical Systems. Series S 3 Nonlinear Analysis. Theory, Methods & Applications 3 Annals of PDE 3 Bollettino dell’Unione Matematica Italiana 2 Journal of Computational Physics 2 Russian Mathematical Surveys 2 Mathematics of Computation 2 Bulletin of Mathematical Biology 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Journal of Optimization Theory and Applications 2 Monatshefte für Mathematik 2 Results in Mathematics 2 Applied Mathematics and Mechanics. (English Edition) 2 The Journal of Geometric Analysis 2 Bulletin of the American Mathematical Society. New Series 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Physics of Fluids ...and 100 more Serials
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#### Cited in 45 Fields

 771 Partial differential equations (35-XX) 380 Dynamical systems and ergodic theory (37-XX) 211 Fluid mechanics (76-XX) 74 Ordinary differential equations (34-XX) 68 Mechanics of particles and systems (70-XX) 51 Statistical mechanics, structure of matter (82-XX) 50 Optics, electromagnetic theory (78-XX) 45 Mechanics of deformable solids (74-XX) 40 Numerical analysis (65-XX) 38 Quantum theory (81-XX) 33 Operator theory (47-XX) 27 Biology and other natural sciences (92-XX) 22 Global analysis, analysis on manifolds (58-XX) 19 Systems theory; control (93-XX) 16 Probability theory and stochastic processes (60-XX) 15 Integral equations (45-XX) 12 Differential geometry (53-XX) 10 Geophysics (86-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Difference and functional equations (39-XX) 8 Functional analysis (46-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Manifolds and cell complexes (57-XX) 5 Relativity and gravitational theory (83-XX) 4 Functions of a complex variable (30-XX) 3 Special functions (33-XX) 3 Computer science (68-XX) 2 History and biography (01-XX) 2 Commutative algebra (13-XX) 2 Topological groups, Lie groups (22-XX) 2 Real functions (26-XX) 2 Sequences, series, summability (40-XX) 2 Approximations and expansions (41-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)