Communications on Pure and Applied Mathematics · 1996 · 102 citations · 23 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsMathematical PhysicsIntegrable SystemsNonlinear DynamicsPerturbation MethodsPerturbation TheorySchrödinger EquationSingular Perturbation TheoryGeometric Singular Perturbation TheoryHomoclinic OrbitsNonlinear Schrödinger EquationPeriodic Boundary ConditionsPeriodic Orbit PersistencePeriodic Orbits In Hamiltonian SystemsPeriodic Solutions Of Differential EquationsSingular Perturbation Analysis
The persistence of homoclinic orbits for certain perturbations of the integrable nonlinear Schrödinger equation under even periodic boundary conditions is established. More specifically, the existence of a symmetric pair of homoclinic orbits is established for the perturbed NLS equation through an argument that combines Melnikov analysis with a geometric singular perturbation theory for the PDE. © 1996 John Wiley & Sons, Inc.
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Ordinary Differential Equations.
Ray Redheffer, Jack K. Hale · American Mathematical Monthly · 1971 · 2.2K citations
Invariant manifolds for flows in Banach spaces
Shui-Nee Chow, Kening Lu · Journal of Differential Equations · 1988 · 275 citations