Stable NLS solitons in a cubic–quintic medium with a delta-function potential. (March 2016)

• Record Type: Journal Article
• Authors: Genoud, François; Malomed, Boris A.; Weishäupl, Rada M.
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 28
• Page End: 50
• Publication Date: 2016-03
• Subjects: 35J60 -- 35B32 -- 35Q55 -- 37C75 -- 74J30 -- 78A60; Nonlinear Schrödinger equation -- Cubic–quintic nonlinearity -- Trapping delta potential -- Bifurcation -- Stability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.11.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the one-dimensional nonlinear Schrödinger equation with the cubic–quintic combination of attractive and repulsive nonlinearities, and a trapping potential represented by a delta-function. We determine all bound states with a positive soliton profile through explicit formulas and, using bifurcation theory, we describe their behavior with respect to the propagation constant. This information is used to prove their stability by means of the rigorous theory of orbital stability of Hamiltonian systems. The presence of the trapping potential gives rise to a regime where two stable bound states coexist, with different powers and same propagation constant.