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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.

journal of mathematical physics

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