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.
|Number of pages||23|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|State||Published - Mar 2016|
- Cubic-quintic nonlinearity
- Nonlinear Schrödinger equation
- Trapping delta potential