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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 979252, 7 pages
http://dx.doi.org/10.1155/2013/979252
Research Article

Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term

Rui Cao1,2

1Department of Mathematics, Heze University, Heze 274000, China
2College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China

Received 12 July 2013; Accepted 10 September 2013

Academic Editor: Yong Hong Wu

Copyright © 2013 Rui Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation. We investigate the exact travelling wave solutions of the nonlinear Schrödinger equation using three methods, namely, the auxiliary equation method, the first integral method, and the direct integral method. As a result, Jacobi elliptic function solution, hyperbolic function solution, trigonometric function solution, and rational solution with parameters are obtained successfully. When the parameters are taken as special values, the two known solitary wave solution and periodic wave solution are derived from the solutions obtained. The aim of the paper is to compare the efficiency of the three methods.