Soliton solutions for variable coefficient nonlinear Schr?dinger equation for optical fiber and their application

Abstract

In this paper, the general variable coefficient nonlinear Schrdinger equation for the optical fiber is investigated based on the extended cubic nonlinear Klein-Gordon equation. The soliton solutions under non-chirp case are discussed, and some new exact solutions, including the bright soliton, the dark soliton and the soliton-like solution are obtained. The standard nonlinear Schrdinger equation and four kinds of the variable coefficient nonlinear Schrdinger equation are all corresponding special cases. In addition, some interesting results for the optical fiber system with periodic gain or loss are also obtained.