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

Francois Genoud, Boris A. Malomed, Rada M. Weishäupl

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)28-50
Number of pages23
JournalNonlinear Analysis: Theory, Methods & Applications
Publication statusPublished - 2016


  • Nonlinear Schrödinger equation
  • Cubic–quintic nonlinearity
  • Trapping delta potential
  • Bifurcation
  • Stability


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