Soliton solutions in the modified nonlinear Schrödinger equation in inhomogeneous optical fibers and non-uniform proteins

Abstract

A variable-coefficient modified nonlinear Schrödinger equation is introduced to describe dynamics of optical wave in inhomogeneous optical fibers and travelling wave in the non-uniform alpha-helical proteins. A correlation between the variable-coefficient modified nonlinear Schrödinger equation and the constant cubic–quintic one is presented. Based on solutions of the constant cubic–quintic nonlinear Schrödinger equation, we get explicit solutions of the variable-coefficient modified nonlinear Schrödinger equation.