On the Existence of Dark Solitons in a Cubic-Quintic Nonlinear Schrödinger Equation with a Periodic Potential

摘要

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