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

摘要

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