Exact Traveling Wave Solutions for Higher Order Nonlinear Schrödinger Equations in Optics by Using the (G'/G, 1/G)-expansion Method

Abstract

" The propagation of the optical solitons is usually governed by the nonlinear Schr\u00f6dinger equations. In this article, the two variable (G'\/G, 1\/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear Schr\u00f6dinger equations describing the propagation of femtosecond pulses in nonlinear optical fibers. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations rediscovered from the traveling waves. Thismethod can be thought of as the generalization of well-known original (G'\/G)-expansion method proposed by M. Wang et al. It is shown that the two variable (G'\/G, 1\/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics."