Homoclinic orbits and chaos in discretized perturbed NLS systems. I: Homoclinic orbits

DOI10.1007/BF02678088zbMath0870.35093MaRDI QIDQ1356123

Y. Charles Li, David W. McLaughlin

Publication date: 27 August 1997

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

spectral theoryMelnikov analysishomoclinic orbitsdiscrete nonlinear Schrödinger equationFenchel fiberspersistent invariant manifolds

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Cites Work

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• Geometric singular perturbation theory for ordinary differential equations
• Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation
• Orbits homoclinic to resonances: The Hamiltonian case
• Morse and Melnikov functions for NLS PDE's
• The stable, center-stable, center, center-unstable, unstable manifolds
• A Nonlinear Difference Scheme and Inverse Scattering
• Correlations between Chaos in a Perturbed Sine-Gordon Equation and a Truncated Model System
• Invariant manifolds

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