Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities

Dirk Hundertmark, Young Ran Lee, Tobias Ried, Vadim Zharnitsky

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)3311-3338
Number of pages28
JournalJournal of Differential Equations
Volume265
Issue number8
DOIs
StatePublished - Oct 15 2018

Keywords

  • Nonlocal NLS
  • Nonlocal variational problems
  • Saturated nonlinearities
  • Solitary waves

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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