Solitons for the cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

Abstract

In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic–quintic nonlinear Schrödinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose–Einstein condensates and nonlinear optics.