A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schrödinger Equations

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dc.creatorGesztesy, F.
dc.creatorJones, C. K. R. T.
dc.creatorLatushkin, Y.
dc.creatorStanislavova, M.
dc.date1999-07-17
dc.date.accessioned2026-07-07T06:17:51Z
dc.date.available2026-07-07T06:17:51Z
dc.descriptionA spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schr\" odinger type equations. The theorem is applied to the operator that arises as the linearization of the equation around a standing wave solution. We cast the problem in the context of space-dependent nonlinearities that arise in optical waveguide problems. The result is, however, more generally applicable including to equations in higher dimensions and even systems. The consequence is that stable, unstable, and center manifolds exist in the neighborhood of a (stable or unstable) standing wave, such as a waveguide mode, under simple and commonly verifiable spectral conditions.
dc.descriptionLaTeX, 16 pages
dc.identifierhttps://arxiv.org/abs/solv-int/9907017
dc.identifierhttp://arxiv.org/abs/solv-int/9907017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94534
dc.subjectExactly Solvable and Integrable Systems
dc.titleA Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schrödinger Equations
dc.typetext

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