On existence of dark solitons in cubic-quintic nonlinear Schrödinger equation with a periodic potential

Abstract

A proof of existence of stationary dark soliton solutions of the cubic-quintic nonlinear Schrödinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic on the Poincaré map.

arXiv comment10 pages

References in corpus (3)

• Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices
• Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential
• Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices

Cited by in corpus (1)

• Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials