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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.