Stable NLS solitons in a cubic-quintic medium with a delta-function potential
Analysis of PDEs
2015-11-10 v3 Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
Optics
Abstract
We study the one-dimensional nonlinear Schr\"odinger 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.
Cite
@article{arxiv.1409.6511,
title = {Stable NLS solitons in a cubic-quintic medium with a delta-function potential},
author = {François Genoud and Boris A. Malomed and Rada M. Weishäupl},
journal= {arXiv preprint arXiv:1409.6511},
year = {2015}
}
Comments
22 pages, 8 figures, mistake fixed in the proof of Theorem 3