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 -