Edit Profile (opens in new tab) Wayne, Clarence Eugene Co-Author Distance Author ID: wayne.c-eugene Published as: Wayne, C. Eugene; Wayne, C. E.; Wayne, Clarence Eugene; Wayne, E. more...less External Links: MGP · Wikidata · Google Scholar · dblp · GND Documents Indexed: 92 Publications since 1983, including 1 Book and 1 Additional arXiv Preprint 1 Contribution as Editor Co-Authors: 68 Co-Authors with 81 Joint Publications 2,105 Co-Co-Authors all top 5 Co-Authors 12 single-authored 11 Eckmann, Jean-Pierre 9 Schneider, Guido 7 Beck, Margaret 7 Gallay, Thierry 5 Craig, Walter 5 Hoffman, Aaron 4 de la Llave, Rafael 2 Banyaga, Augustin 2 Chaudhary, Osman 2 Fröhlich, Jürg Martin 2 Goh, Ryan N. 2 Krigman, S. S. 2 Schäfer, Tobias 2 Spencer, Thomas C. 2 Uminsky, David T. 2 Zharnitsky, Vadim 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 Caballero, Daniel A. 1 Chen, Goong 1 Chirilus-Bruckner, Martina 1 Chueshov, Igor’ Dmitrievich 1 Chung, Yeojin 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 Guyenne, Philippe 1 Hall, Glen Richard 1 Jackson, Russell K. 1 Jones, Christopher K. R. T. 1 Josić, Krešimir 1 Kappeler, Thomas 1 Krantz, Steven George 1 Kuksin, Sergeĭ B. 1 Levermore, C. David 1 Matthies, Karsten 1 McQuighan, Kelly 1 Nagem, Raymond J. 1 Norton, Trevor 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 Shirikyan, Armen R. 1 Sulem, Catherine 1 Thomas, Lawrence E. 1 van Baalen, Guillaume 1 Weinstein, Michael I. 1 Welter, Roland 1 West, Harry H. 1 Wittwer, Peter 1 Wright, J. Douglas all top 5 Serials 12 Communications in Mathematical Physics 7 Nonlinearity 5 Archive for Rational Mechanics and Analysis 5 Journal of Mathematical Analysis and Applications 5 SIAM Journal on Applied Dynamical Systems 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 3 Discrete and Continuous Dynamical Systems 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 Indiana University Mathematics Journal 1 Mathematische Zeitschrift 1 Quarterly of Applied Mathematics 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 Experimental Mathematics 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 Lectures in Applied Mathematics 1 Frontiers in Applied Dynamical Systems: Reviews and Tutorials all top 5 Fields 62 Partial differential equations (35-XX) 31 Dynamical systems and ergodic theory (37-XX) 29 Fluid mechanics (76-XX) 9 Ordinary differential equations (34-XX) 7 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 Real functions (26-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 78 Publications have been cited 2,065 times in 1,468 Documents Cited by ▼ Year ▼ Newton’s method and periodic solutions of nonlinear wave equations. Zbl 0794.35104 Craig, Walter; Wayne, C. Eugene 269 1993 Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Zbl 0708.35087 Wayne, C. Eugene 255 1990 Propagation of ultra-short optical pulses in cubic nonlinear media. Zbl 1054.81554 Schäfer, T.; Wayne, C. E. 213 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 104 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 94 2000 Ultra-short pulses in linear and nonlinear media. Zbl 1125.35412 Chung, Y.; Jones, C. K. R. T.; Schäfer, T.; Wayne, C. E. 92 2005 Global stability of vortex solutions of the two-dimensional Navier-Stokes equation. Zbl 1139.35084 Gallay, Thierry; Wayne, C. Eugene 79 2005 Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier-Stokes equations. Zbl 1296.35114 Beck, Margaret; Wayne, C. Eugene 59 2013 Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations. Zbl 0890.35016 Pillet, Claude-Alain; Wayne, C. Eugene 57 1997 Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model. Zbl 0970.35126 Schneider, Guido; Wayne, C. Eugene 56 2000 Localization in disordered, nonlinear dynamical systems. Zbl 0629.60105 Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene 55 1986 The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006 Schneider, Guido; Wayne, C. Eugene 50 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 33 2002 Propagating fronts and the center manifold theorem. Zbl 0790.34045 Eckmann, J.-P.; Wayne, C. E. 29 1991 Kawahara dynamics in dispersive media. Zbl 0977.35123 Schneider, Guido; Wayne, C. Eugene 29 2001 Invariant manifolds for parabolic partial differential equations on unbounded domains. Zbl 0882.35061 Wayne, C. Eugene 27 1997 On Irwin’s proof of the pseudostable manifold theorem. Zbl 0843.58100 de la Llave, Rafael; Wayne, C. Eugene 26 1995 Cohomology equations near hyperbolic points and geometric versions of Sternberg linearization theorem. Zbl 0918.53016 Banyaga, A.; de la Llave, R.; Wayne, C. E. 26 1996 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 24 2016 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. 23 1989 Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178 Schneider, Guido; Wayne, C. Eugene 23 2011 The nonlinear stability of front solutions for parabolic partial differential equations. Zbl 0817.35036 Eckmann, Jean-Pierre; Wayne, C. Eugene 22 1994 Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349 de la Llave, R.; Wayne, C. E. 18 2004 Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice. Zbl 1153.82323 Hoffman, A.; Wayne, C. E. 17 2008 On the validity of mean-field amplitude equations for counterpropagating wavetrains. Zbl 0833.35128 Pierce, R. D.; Wayne, C. E. 16 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. 15 1995 Mathematical aspects of surface water waves. Zbl 1203.76023 Craig, W.; Wayne, C. E. 15 2007 Existence and stability of traveling pulses in a continuous neuronal network. Zbl 1091.45004 Pinto, David J.; Jackson, Russell K.; Wayne, C. Eugene 15 2005 Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model. Zbl 1172.35066 Hoffman, Aaron; Wayne, C. E. 15 2009 Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation. Zbl 0912.35140 Eckmann, Jean-Pierre; Wayne, C. Eugene; Wittwer, Peter 13 1997 Existence and stability of traveling fronts in the extended Fisher-Kolmogorov equation. Zbl 1109.35361 Rottschäfer, V.; Wayne, C. E. 13 2001 Liapunov spectra for infinite chains of nonlinear oscillators. Zbl 1084.37500 Eckmann, Jean-Pierre; Wayne, C. Eugene 11 1988 Dynamics of partial differential equations. Zbl 1331.35006 Wayne, C. Eugene; Weinstein, Michael I. 11 2015 The KAM theory of systems with short range interactions. I. Zbl 0585.58023 Wayne, C. Eugene 11 1984 Existence and stability of asymmetric Burgers vortices. Zbl 1119.76012 Gallay, Thierry; Wayne, C. Eugene 11 2007 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 11 2012 Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1201.35044 Beck, Margaret; Wayne, C. Eugene 11 2009 Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1227.35061 Beck, Margaret; Wayne, C. Eugene 10 2011 Relative equilibria of the \((1+N)\)-vortex problem. Zbl 1329.76047 Barry, Anna M.; Hall, Glen R.; Wayne, C. Eugene 9 2012 On the validity of 2D surface water wave models. Zbl 1096.76504 Schneider, Guido; Wayne, C. Eugene 9 2002 An introduction to KAM theory. Zbl 0844.58037 Wayne, C. Eugene 8 1996 Higher-order modulation equations for a Boussinesq equation. Zbl 1088.76007 Wayne, C. Eugene; Wright, J. Douglas 8 2002 Bounds on the trajectories of a system of weakly coupled rotators. Zbl 0615.70013 Wayne, C. Eugene 8 1986 Generalized Helmholtz-Kirchhoff model for two-dimensional distributed vortex motion. Zbl 1408.76205 Nagem, Raymond; Sandri, Guido; Uminsky, David; Wayne, C. Eugene 8 2009 Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401 Schneider, Guido; Wayne, C. Eugene 7 2003 Boundary controllability of Maxwell’s equations with nonzero conductivity inside a cube. I. Spectral controllability. Zbl 1154.93317 Krigman, S. S.; Wayne, C. E. 7 2007 Vortices and two-dimensional fluid motion. Zbl 1372.76002 Wayne, C. Eugene 7 2011 Rigorous justification of Taylor dispersion via center manifolds and hypocoercivity. Zbl 1434.35085 Beck, Margaret; Chaudhary, Osman; Wayne, C. Eugene 7 2020 Phase slips and the Eckhaus instability. Zbl 0846.35032 Eckmann, J.-P.; Gallay, Th.; Wayne, C. E. 6 1995 Modified energy functionals and the NLS approximation. Zbl 1375.35406 Wayne, C. Eugene; Cummings, Patrick 6 2017 Asymptotic stability of the Toda \(m\)-soliton. Zbl 1226.82006 Benes, G. N.; Hoffman, A.; Wayne, C. E. 6 2012 A multi-moment vortex method for 2D viscous fluids. Zbl 1408.76210 Uminsky, David; Wayne, C. Eugene; Barbaro, Alethea 6 2012 On the elimination of non-resonance harmonics. Zbl 0596.58021 Wayne, C. Eugene 6 1986 Three-dimensional stability of Burgers vortices: the low Reynolds number case. Zbl 1091.35080 Gallay, Thierry; Wayne, C. Eugene 6 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 6 2006 Orbital stability of localized structures via Bäcklund transformations. Zbl 1289.35225 Hoffman, Aaron; Wayne, C. Eugene 6 2013 Normal forms for parabolic partial differential equations. Zbl 0791.35057 Eckmann, J.-P.; Epstein, H.; Wayne, C. E. 5 1993 Cohomology equations and commutators of germs of contact diffeomorphisms. Zbl 0671.58031 Banyaga, Augustin; de la Llave, Rafael; Wayne, C. Eugene 5 1989 The largest Lyapunov exponent for random matrices and directed polymers in a random environment. Zbl 0673.60066 Eckmann, J.-P.; Wayne, C. E. 5 1989 Energy dissipation in Hamiltonian chains of rotators. Zbl 1456.37065 Cuneo, Noé; Eckmann, Jean-Pierre; Wayne, C. Eugene 5 2017 On the stability of dense point spectrum for self-adjoint operators. Zbl 0608.47018 Thomas, Lawrence E.; Wayne, C. Eugene 5 1986 Breathers as metastable states for the discrete NLS equation. Zbl 1524.34034 Eckmann, Jean-Pierre; Wayne, C. Eugene 4 2018 Periodic solutions of nonlinear partial differential equations. Zbl 0912.35016 Wayne, C. Eugene 4 1997 Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem. Zbl 1325.34021 Chirilus-Bruckner, Martina; Wayne, Clarence Eugene 4 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 4 2012 The KAM theory of systems with short range interactions. II. Zbl 0595.58022 Wayne, C. Eugene 4 1984 Analysis of enhanced diffusion in Taylor dispersion via a model problem. Zbl 1331.35270 Beck, Margaret; Chaudhary, Osman; Wayne, C. Eugene 4 2015 Nonlinear waves and the \(1:1:2\) resonance. Zbl 0849.35133 Craig, Walter; Wayne, C. Eugene 3 1994 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. 3 2007 Wave pinning in strips. Zbl 1119.35027 Matthies, Karsten; Wayne, C. E. 3 2006 Decay of Hamiltonian breathers under dissipation. Zbl 1477.35239 Eckmann, Jean-Pierre; Wayne, C. Eugene 3 2020 Dynamics of a ring of diffusively coupled Lorenz oscillators. Zbl 0996.37037 Josić, Krešimir; Wayne, C. Eugene 2 2000 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 2 2016 Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws. Zbl 1145.35081 Beck, Margaret; Wayne, C. Eugene 2 2008 Vortices in stably-stratified rapidly rotating Boussinesq convection. Zbl 1414.35167 Goh, Ryan; Wayne, C. Eugene 2 2019 Critical points of Strichartz functional. Zbl 1473.35038 Wayne, C. Eugene; Zharnitsky, Vadim 2 2021 Long tails in the long-time asymptotics of quasi-linear hyperbolic-parabolic systems of conservation laws. Zbl 1172.35332 van Baalen, Guillaume; Popović, Nikola; Wayne, C. Eugene 1 2008 An invariant torus for nearly integrable Hamiltonian systems with infinitely many degrees of freedom. Zbl 0618.58019 Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene 1 1986 Critical points of Strichartz functional. Zbl 1473.35038 Wayne, C. Eugene; Zharnitsky, Vadim 2 2021 Rigorous justification of Taylor dispersion via center manifolds and hypocoercivity. Zbl 1434.35085 Beck, Margaret; Chaudhary, Osman; Wayne, C. Eugene 7 2020 Decay of Hamiltonian breathers under dissipation. Zbl 1477.35239 Eckmann, Jean-Pierre; Wayne, C. Eugene 3 2020 Vortices in stably-stratified rapidly rotating Boussinesq convection. Zbl 1414.35167 Goh, Ryan; Wayne, C. Eugene 2 2019 Breathers as metastable states for the discrete NLS equation. Zbl 1524.34034 Eckmann, Jean-Pierre; Wayne, C. Eugene 4 2018 Modified energy functionals and the NLS approximation. Zbl 1375.35406 Wayne, C. Eugene; Cummings, Patrick 6 2017 Energy dissipation in Hamiltonian chains of rotators. Zbl 1456.37065 Cuneo, Noé; Eckmann, Jean-Pierre; Wayne, C. Eugene 5 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 24 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 2 2016 Dynamics of partial differential equations. Zbl 1331.35006 Wayne, C. Eugene; Weinstein, Michael I. 11 2015 Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem. Zbl 1325.34021 Chirilus-Bruckner, Martina; Wayne, Clarence Eugene 4 2015 Analysis of enhanced diffusion in Taylor dispersion via a model problem. Zbl 1331.35270 Beck, Margaret; Chaudhary, Osman; Wayne, C. Eugene 4 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 59 2013 Orbital stability of localized structures via Bäcklund transformations. Zbl 1289.35225 Hoffman, Aaron; Wayne, C. Eugene 6 2013 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 11 2012 Relative equilibria of the \((1+N)\)-vortex problem. Zbl 1329.76047 Barry, Anna M.; Hall, Glen R.; Wayne, C. Eugene 9 2012 Asymptotic stability of the Toda \(m\)-soliton. Zbl 1226.82006 Benes, G. N.; Hoffman, A.; Wayne, C. E. 6 2012 A multi-moment vortex method for 2D viscous fluids. Zbl 1408.76210 Uminsky, David; Wayne, C. Eugene; Barbaro, Alethea 6 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 4 2012 Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178 Schneider, Guido; Wayne, C. Eugene 23 2011 Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1227.35061 Beck, Margaret; Wayne, C. Eugene 10 2011 Vortices and two-dimensional fluid motion. Zbl 1372.76002 Wayne, C. Eugene 7 2011 Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model. Zbl 1172.35066 Hoffman, Aaron; Wayne, C. E. 15 2009 Using global invariant manifolds to understand metastability in the Burgers equation with small viscosity. Zbl 1201.35044 Beck, Margaret; Wayne, C. Eugene 11 2009 Generalized Helmholtz-Kirchhoff model for two-dimensional distributed vortex motion. Zbl 1408.76205 Nagem, Raymond; Sandri, Guido; Uminsky, David; Wayne, C. Eugene 8 2009 Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice. Zbl 1153.82323 Hoffman, A.; Wayne, C. E. 17 2008 Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws. Zbl 1145.35081 Beck, Margaret; Wayne, C. Eugene 2 2008 Long tails in the long-time asymptotics of quasi-linear hyperbolic-parabolic systems of conservation laws. Zbl 1172.35332 van Baalen, Guillaume; Popović, Nikola; Wayne, C. Eugene 1 2008 Mathematical aspects of surface water waves. Zbl 1203.76023 Craig, W.; Wayne, C. E. 15 2007 Existence and stability of asymmetric Burgers vortices. Zbl 1119.76012 Gallay, Thierry; Wayne, C. Eugene 11 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. 7 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. 3 2007 Three-dimensional stability of Burgers vortices: the low Reynolds number case. Zbl 1091.35080 Gallay, Thierry; Wayne, C. Eugene 6 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 6 2006 Wave pinning in strips. Zbl 1119.35027 Matthies, Karsten; Wayne, C. E. 3 2006 Ultra-short pulses in linear and nonlinear media. Zbl 1125.35412 Chung, Y.; Jones, C. K. R. T.; Schäfer, T.; Wayne, C. E. 92 2005 Global stability of vortex solutions of the two-dimensional Navier-Stokes equation. Zbl 1139.35084 Gallay, Thierry; Wayne, C. Eugene 79 2005 Existence and stability of traveling pulses in a continuous neuronal network. Zbl 1091.45004 Pinto, David J.; Jackson, Russell K.; Wayne, C. Eugene 15 2005 Propagation of ultra-short optical pulses in cubic nonlinear media. Zbl 1054.81554 Schäfer, T.; Wayne, C. E. 213 2004 Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349 de la Llave, R.; Wayne, C. E. 18 2004 Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401 Schneider, Guido; Wayne, C. Eugene 7 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 104 2002 The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006 Schneider, Guido; Wayne, C. Eugene 50 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 33 2002 On the validity of 2D surface water wave models. Zbl 1096.76504 Schneider, Guido; Wayne, C. Eugene 9 2002 Higher-order modulation equations for a Boussinesq equation. Zbl 1088.76007 Wayne, C. Eugene; Wright, J. Douglas 8 2002 Kawahara dynamics in dispersive media. Zbl 0977.35123 Schneider, Guido; Wayne, C. Eugene 29 2001 Existence and stability of traveling fronts in the extended Fisher-Kolmogorov equation. Zbl 1109.35361 Rottschäfer, V.; Wayne, C. E. 13 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 94 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 56 2000 Dynamics of a ring of diffusively coupled Lorenz oscillators. Zbl 0996.37037 Josić, Krešimir; Wayne, C. Eugene 2 2000 Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations. Zbl 0890.35016 Pillet, Claude-Alain; Wayne, C. Eugene 57 1997 Invariant manifolds for parabolic partial differential equations on unbounded domains. Zbl 0882.35061 Wayne, C. Eugene 27 1997 Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation. Zbl 0912.35140 Eckmann, Jean-Pierre; Wayne, C. Eugene; Wittwer, Peter 13 1997 Periodic solutions of nonlinear partial differential equations. Zbl 0912.35016 Wayne, C. Eugene 4 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. 26 1996 An introduction to KAM theory. Zbl 0844.58037 Wayne, C. Eugene 8 1996 On Irwin’s proof of the pseudostable manifold theorem. Zbl 0843.58100 de la Llave, Rafael; Wayne, C. Eugene 26 1995 On the validity of mean-field amplitude equations for counterpropagating wavetrains. Zbl 0833.35128 Pierce, R. D.; Wayne, C. E. 16 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. 15 1995 Phase slips and the Eckhaus instability. Zbl 0846.35032 Eckmann, J.-P.; Gallay, Th.; Wayne, C. E. 6 1995 The nonlinear stability of front solutions for parabolic partial differential equations. Zbl 0817.35036 Eckmann, Jean-Pierre; Wayne, C. Eugene 22 1994 Nonlinear waves and the \(1:1:2\) resonance. Zbl 0849.35133 Craig, Walter; Wayne, C. Eugene 3 1994 Newton’s method and periodic solutions of nonlinear wave equations. Zbl 0794.35104 Craig, Walter; Wayne, C. Eugene 269 1993 Normal forms for parabolic partial differential equations. Zbl 0791.35057 Eckmann, J.-P.; Epstein, H.; Wayne, C. E. 5 1993 Propagating fronts and the center manifold theorem. Zbl 0790.34045 Eckmann, J.-P.; Wayne, C. E. 29 1991 Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Zbl 0708.35087 Wayne, C. Eugene 255 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. 23 1989 Cohomology equations and commutators of germs of contact diffeomorphisms. Zbl 0671.58031 Banyaga, Augustin; de la Llave, Rafael; Wayne, C. Eugene 5 1989 The largest Lyapunov exponent for random matrices and directed polymers in a random environment. Zbl 0673.60066 Eckmann, J.-P.; Wayne, C. E. 5 1989 Liapunov spectra for infinite chains of nonlinear oscillators. Zbl 1084.37500 Eckmann, Jean-Pierre; Wayne, C. Eugene 11 1988 Localization in disordered, nonlinear dynamical systems. Zbl 0629.60105 Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene 55 1986 Bounds on the trajectories of a system of weakly coupled rotators. Zbl 0615.70013 Wayne, C. Eugene 8 1986 On the elimination of non-resonance harmonics. Zbl 0596.58021 Wayne, C. Eugene 6 1986 On the stability of dense point spectrum for self-adjoint operators. Zbl 0608.47018 Thomas, Lawrence E.; Wayne, C. Eugene 5 1986 An invariant torus for nearly integrable Hamiltonian systems with infinitely many degrees of freedom. Zbl 0618.58019 Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene 1 1986 The KAM theory of systems with short range interactions. I. Zbl 0585.58023 Wayne, C. Eugene 11 1984 The KAM theory of systems with short range interactions. II. Zbl 0595.58022 Wayne, C. Eugene 4 1984 all cited Publications top 5 cited Publications all top 5 Cited by 1,562 Authors 41 Schneider, Guido 35 Wayne, Clarence Eugene 31 Geng, Jiansheng 28 Procesi, Michela 25 Berti, Massimiliano 23 Bambusi, Dario 23 Gallay, Thierry 21 de la Llave, Rafael 20 Ji, Shuguan 18 Yuan, Xiaoping 17 Bedrossian, Jacob 16 Düll, Wolf-Patrick 16 Pelinovsky, Dmitry Efimovich 14 Coclite, Giuseppe Maria 14 Maekawa, Yasunori 14 Montalto, Riccardo 13 Coti Zelati, Michele 13 Cuccagna, Scipio 13 Di Ruvo, Lorenzo 13 Feng, Baofeng 13 Scheel, Arnd 13 Si, Jianguo 13 Xu, Junxiang 12 Gao, Meina 12 Li, Yong 11 Kevrekidis, Panayotis G. 11 Lou, Zhaowei 11 Masmoudi, Nader 11 Qu, Changzheng 11 Zhang, Min 11 Zhang, Zhifei 10 Bona, Jerry Lloyd 10 Cong, Hongzi 10 Liu, Yue 10 Shi, Yanling 10 Wright, J. Douglas 10 Xu, XinDong 9 Biasco, Luca 9 Bolle, Philippe 9 Craig, Walter 9 Liu, Jianjun 9 Stefanov, Atanas G. 9 Wei, Hui 8 Eckmann, Jean-Pierre 8 Gao, Yixian 8 Gentile, Guido 8 Grébert, Benoît 8 Kalisch, Henrik 8 Komech, Alexander Ilich 8 Mi, Lufang 8 Pu, Xueke 8 Wei, Dongyi 8 You, Jiangong 7 Chirilus-Bruckner, Martina 7 Fu, Ying 7 Germain, Pierre 7 Goh, Ryan N. 7 Kopylova, Elena A. 7 Lannes, David 7 Matthies, Karsten 7 Sulem, Catherine 7 Sun, Yingnan 7 Uecker, Hannes 7 Xue, Shuaishuai 6 Albritton, Dallas 6 Beck, Margaret 6 Brandolese, Lorenzo 6 Corsi, Livia 6 Fan, Engui 6 Feola, Roberto 6 Guardia, Marcel 6 Israwi, Samer 6 Ohta, Yasuhiro 6 Rui, Jie 6 Shen, Shoufeng 6 Šverák, Vladimír 6 Wang, Wei-Min 6 Wang, Yi 6 Weinstein, Michael I. 6 Yan, Dongfeng 5 Avery, Montie 5 Baldi, Pietro 5 Bourgain, Jean 5 Brunelli, J. C. 5 Chen, Bochao 5 Chierchia, Luigi 5 Chong, Christopher 5 Faye, Grégory 5 Fontich, Ernest 5 Giuliani, Filippo 5 Guo, Yanfeng 5 Hadadifard, Fazel 5 Haller, George 5 Haus, Emanuele 5 Herrmann, Michael 5 Holzer, Matt 5 Kaloshin, Vadim Yu. 5 Li, Jibin 5 Liu, Huimin 5 Maeda, Masaya ...and 1,462 more Authors all top 5 Cited in 254 Serials 114 Journal of Differential Equations 81 Communications in Mathematical Physics 77 Physica D 51 Archive for Rational Mechanics and Analysis 46 Journal of Dynamics and Differential Equations 41 Journal of Mathematical Physics 35 Journal of Mathematical Analysis and Applications 34 Discrete and Continuous Dynamical Systems 26 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 25 Nonlinearity 24 Journal of Functional Analysis 23 Journal of Nonlinear Science 20 SIAM Journal on Mathematical Analysis 19 Journal of Statistical Physics 19 Journal of Mathematical Fluid Mechanics 18 Mathematical Methods in the Applied Sciences 18 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 18 Communications in Partial Differential Equations 16 Applicable Analysis 16 Communications on Pure and Applied Mathematics 16 SIAM Journal on Applied Dynamical Systems 15 Studies in Applied Mathematics 15 Chaos 15 Communications in Nonlinear Science and Numerical Simulation 14 Physics Letters. A 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 Advances in Mathematics 12 Transactions of the American Mathematical Society 12 Regular and Chaotic Dynamics 11 Theoretical and Mathematical Physics 11 Memoirs of the American Mathematical Society 11 Boundary Value Problems 10 Wave Motion 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Applied Mathematics and Computation 9 Inventiones Mathematicae 9 Applied Mathematics Letters 9 Qualitative Theory of Dynamical Systems 9 Discrete and Continuous Dynamical Systems. Series B 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Journal of Nonlinear Mathematical Physics 8 Nonlinear Analysis. Real World Applications 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Journal of Fluid Mechanics 7 Duke Mathematical Journal 7 Quarterly of Applied Mathematics 7 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 7 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 7 Communications on Pure and Applied Analysis 7 Science China. Mathematics 6 Chaos, Solitons and Fractals 6 Journal of Computational and Applied Mathematics 6 Mathematische Annalen 6 Mathematische Zeitschrift 6 Nonlinear Dynamics 6 Annales Henri Poincaré 6 Discrete and Continuous Dynamical Systems. Series S 6 Journal of Applied Analysis and Computation 5 Journal of Computational Physics 5 Mathematics and Computers in Simulation 5 Proceedings of the American Mathematical Society 5 Chinese Annals of Mathematics. Series B 5 Acta Applicandae Mathematicae 5 SIAM Journal on Applied Mathematics 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Calculus of Variations and Partial Differential Equations 5 NoDEA. Nonlinear Differential Equations and Applications 5 Journal of the European Mathematical Society (JEMS) 5 Oberwolfach Reports 5 Analysis & PDE 5 Water Waves 4 Physica A 4 Reviews in Mathematical Physics 4 Journal of Geometry and Physics 4 Indiana University Mathematics Journal 4 Journal of the London Mathematical Society. Second Series 4 Siberian Mathematical Journal 4 Systems & Control Letters 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Annales de l’Institut Henri Poincaré. Physique Théorique 4 Journal of Mathematical Sciences (New York) 4 Journal of High Energy Physics 4 Advanced Nonlinear Studies 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 Journal of Physics A: Mathematical and Theoretical 4 Annals of PDE 4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Letters in Mathematical Physics 3 Reports on Mathematical Physics 3 BIT 3 Mathematische Nachrichten 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Geometric and Functional Analysis. GAFA 3 Turkish Journal of Mathematics 3 Abstract and Applied Analysis 3 Taiwanese Journal of Mathematics 3 European Journal of Mechanics. B. Fluids 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Acta Mathematica Sinica. English Series ...and 154 more Serials all top 5 Cited in 47 Fields 1,145 Partial differential equations (35-XX) 560 Dynamical systems and ergodic theory (37-XX) 335 Fluid mechanics (76-XX) 108 Mechanics of particles and systems (70-XX) 90 Statistical mechanics, structure of matter (82-XX) 88 Ordinary differential equations (34-XX) 78 Optics, electromagnetic theory (78-XX) 60 Mechanics of deformable solids (74-XX) 56 Quantum theory (81-XX) 54 Numerical analysis (65-XX) 43 Operator theory (47-XX) 36 Biology and other natural sciences (92-XX) 33 Global analysis, analysis on manifolds (58-XX) 27 Probability theory and stochastic processes (60-XX) 24 Systems theory; control (93-XX) 21 Integral equations (45-XX) 21 Differential geometry (53-XX) 17 Geophysics (86-XX) 13 Difference and functional equations (39-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 8 Real functions (26-XX) 8 Approximations and expansions (41-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Functional analysis (46-XX) 6 Functions of a complex variable (30-XX) 6 Special functions (33-XX) 6 Computer science (68-XX) 6 Relativity and gravitational theory (83-XX) 5 General and overarching topics; collections (00-XX) 5 Manifolds and cell complexes (57-XX) 3 History and biography (01-XX) 3 Combinatorics (05-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Sequences, series, summability (40-XX) 2 Integral transforms, operational calculus (44-XX) 2 Operations research, mathematical programming (90-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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