Existence of dark solitons in a class of stationary nonlinear Schr\"odinger equations with periodically modulated nonlinearity and periodic asymptotic

Abstract

In this paper, we give a proof of the existence of stationary dark soliton solutions or heteroclinic orbits of nonlinear equations of Schr\"odinger type with periodic inhomogeneous nonlinearity. The result is illustrated with examples of dark solitons for cubic and photorefractive nonlinearities.