TY - JOUR

T1 - Stable NLS solitons in a cubic-quintic medium with a delta-function potential

AU - Genoud, Francois

AU - Malomed, Boris A.

AU - Weishäupl, Rada M.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Nonlinear Schrödinger equation

KW - Cubic–quintic nonlinearity

KW - Trapping delta potential

KW - Bifurcation

KW - Stability

UR - http://resolver.tudelft.nl/uuid://3b768c54-4a4f-4e22-b635-f9d188dcf113

U2 - 10.1016/j.na.2015.11.016

DO - 10.1016/j.na.2015.11.016

M3 - Article

SN - 0362-546X

VL - 133

SP - 28

EP - 50

JO - Nonlinear Analysis: Theory, Methods & Applications

JF - Nonlinear Analysis: Theory, Methods & Applications

ER -