Integrability of an inhomogeneous nonlinear Schrödinger equation in Bose–Einstein condensates and fiber optics

Abstract

In this paper, we investigate the integrability of an inhomogeneous nonlinear Schrödinger equation, which has several applications in many branches of physics, as in Bose–Einstein condensates and fiber optics. The main issue deals with Painlevé property (PP) and Liouville integrability for a nonlinear Schrödinger-type equation. Solutions of the integrable equation are obtained by means of the Darboux transformation. Finally, some applications on fiber optics and Bose–Einstein condensates are proposed (including Bose–Einstein condensates in three-dimensional in cylindrical symmetry).