Bright solitons on a cnoidal wave background for the inhomogeneous nonlinear Schr¨odinger equation

Abstract

In this paper, we investigate the bright solitons on a cnoidal wave background train of the inhomogeneous nonlinear Schr¨odinger equation, which may be applicable to many physically realizable systems such as Bose–Einstein condensation media and plasma, etc. We use well-known methods to reduce the inhomogeneous nonlinear Schr¨odinger equation to a standard nonlinear Schr¨odinger equation by using the combination of Husimi’s and Lens-type transformations. We study the superposed configuration of soliton with a cnoidal wave solution of the underlying equation. Finally, we discuss the dynamics of soliton on a cnoidal wave background in Bose–Einstein condensation trapped in linear density and harmonic density profiles separately.