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arXiv · 1707.06944

Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities

Dirk Hundertmark·Young-Ran Lee·Tobias Ried·Vadim Zharnitsky
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Abstract

A nonlinear Schr\"odinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with periodically varying dispersion profile (dispersion management). The associated constrained variational principle is shown to posses a ground state solution by constructing a convergent minimizing sequence through the application of a method similar to the classical concentration compactness principle of Lions. One of the obstacles in applying this variational approach is that a saturated nonlocal nonlinearity does not satisfy uniformly the so-called strict sub-additivity condition. This is overcome by applying a special version of Ekeland's variational principle.

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Dirk Hundertmark, Young-Ran Lee, Tobias Ried, Vadim Zharnitsky. 2017-07-21. Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities. https://arxiv.org/abs/1707.06944

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