On the existence of dark solitons of the cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity

TL;DR

This paper proves the existence of dark solitons in the defocusing cubic nonlinear Schrödinger equation with periodic inhomogeneous nonlinearity, extending the class of inhomogeneities and exploring related equations.

Contribution

It provides a simple, broad-application proof of dark solitons existence and introduces new properties of these solutions.

Findings

Existence of dark solitons under broader inhomogeneity conditions

New properties of dark soliton solutions

Application to cubic-quintic nonlinear Schrödinger equation with periodic potential

Abstract

We provide a simple proof of the existence of dark solitons of the defocusing cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity. Moreover, our proof allows for a broader class of inhomogeneities and gives some new properties of the solutions. We also apply our approach to the defocusing cubic-quintic nonlinear Schrodinger equation with a periodic potential.