Communications on Pure and Applied Mathematics · 1996 · 10 citations · 0 references
Natural SciencesMathematicsPhysicsComputational PhysicsDifferential EquationsDynamical SystemsIntegrable 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.