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Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities

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


A nonlinear Schrödinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integrodifferential 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.

Volltext §
DOI: 10.5445/IR/1000072733
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000072733
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 24 S.
Serie CRC 1173 ; 2017/19
Schlagwörter saturated nonlinearities, nonlocal NLS, solitary waves, nonlocal variational problems
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