Well–posedness of dispersion managed nonlinear Schrödinger equations

We prove local and global well–posedness results for the Gabitov–Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of nonlinearities and arbitrary average dispersion on L2(R) and H1(R) for zero and non–zero average dispersions, respectively. Moreover, when the average...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 522; no. 1; p. 126938
Main Authors Choi, Mi-Ran, Hundertmark, Dirk, Lee, Young-Ran
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2023
Subjects
Dispersion management
Nonlocal NLS
Orbital stability
Well–posedness
Orbital stability
Nonlocal NLS
Dispersion management
Well–posedness
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Summary:We prove local and global well–posedness results for the Gabitov–Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of nonlinearities and arbitrary average dispersion on L2(R) and H1(R) for zero and non–zero average dispersions, respectively. 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:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126938