A Generalized Sub-Equation Expansion Method and Its Application to the Nonlinear Schrödinger Equation in Inhomogeneous Optical Fiber Media

In this paper, a generalized sub-equation expansion method is presented for constructing some exact analytical solutions of nonlinear partial differential equations. Making use of the method and symbolic computation, we investigate the inhomogeneous nonlinear Schrödinger equation (INLSE) with the loss/gain and the frequency chirping and obtain rich exact analytical solutions. From our results, many known results of some nonlinear Schrödinger equations can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. With computer simulation, the main soliton features of bright and dark solitons, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions are shown by some figures. Nonlinear dynamics of the chirped soliton pulses is also investigated under the different regimes of soliton management. The method developed does provide a systematic way to generate various exact analytical solutions for INLSE with varying coefficients.