## Abstract and Applied Analysis

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

Rui Cao

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 979252, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393443516

Digital Object Identifier
doi:10.1155/2013/979252

Mathematical Reviews number (MathSciNet)
MR3121493

#### Citation

Cao, Rui. Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 979252, 7 pages. doi:10.1155/2013/979252. https://projecteuclid.org/euclid.aaa/1393443516

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