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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.

Reviewer: Alessandro Selvitella (Ottawa)

### MSC:

35Q55 | NLS equations (nonlinear Schrödinger equations) |

35A15 | Variational methods applied to PDEs |

35R09 | Integro-partial differential equations |

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\textit{D. Hundertmark} et al., J. Differ. Equations 265, No. 8, 3311--3338 (2018; Zbl 1395.35173)

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