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

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.

References in corpus (1)

• The heteroclinic connection problem for general double-well potentials