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Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities. (English) Zbl 1395.35173
Authors’ abstract: A nonlinear Schrödinger 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.
MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35A15 Variational methods applied to PDEs
35R09 Integral partial differential equations
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