Well-posedness of dispersion managed nonlinear Schrödinger equations

We prove local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schr\"odinger equation with a large class of nonlinearities and arbitrary average dispersion on \(L^2(\mathbb{R})\) and \(H^1(\mathbb{R})\). Moreover, when the average dispersion is non-neg...

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Bibliographic Details
Published inarXiv.org
Main Authors Choi, Mi-Ran, Hundertmark, Dirk, Young-Ran, Lee
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.12.2022
Subjects
Dispersion
Nonlinear equations
Schrodinger equation
Well posed problems
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Summary:We prove local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schr\"odinger equation with a large class of nonlinearities and arbitrary average dispersion on \(L^2(\mathbb{R})\) and \(H^1(\mathbb{R})\). Moreover, when the average dispersion is non-negative, we show that the set of ground states is orbitally stable. This covers the case of non-saturated and saturated nonlinear polarizations and yields, for saturated nonlinearities, the first proof of orbital stability.
ISSN:2331-8422