Melnikov Analysis for a Singularly Perturbed DSII Equation

DOI10.1111/j.0022-2526.2005.01531.xzbMath1145.37338arXivmath/0206272OpenAlexW2103174084MaRDI QIDQ3528451

Y. Charles Li

Publication date: 16 October 2008

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0206272

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems (37L45) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

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Global dynamics of a pipe conveying pulsating fluid in primary parametrical resonance: analytical and numerical results from the nonlinear wave equation ⋮ Homoclinic degeneracy for perturbed nonlinear Schrödinger equation ⋮ Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate ⋮ Existence of chaos in evolution equations ⋮ Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary

Cites Work

• Smale horseshoes and symbolic dynamics in perturbed nonlinear Schrödinger equations
• Bäcklund-Darboux transformations and Melnikov analysis for Davey-Stewartson II equations
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• On the initial value problem for the Davey-Stewartson systems
• Wave Instabilities

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