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

TL;DR

This paper proves the existence of stationary dark soliton solutions in nonlinear Schrödinger equations with periodic inhomogeneous nonlinearity, supported by examples involving cubic and photorefractive nonlinearities.

Contribution

It provides a rigorous proof of dark soliton existence in a class of nonlinear Schrödinger equations with periodic nonlinearity, expanding understanding of such solutions.

Findings

Existence of dark solitons proven mathematically

Examples demonstrated for cubic and photorefractive nonlinearities

Supports potential applications in nonlinear optics

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.