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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 408586, 10 pages
http://dx.doi.org/10.1155/2015/408586
Research Article

Bifurcation Analysis and Solutions of a Higher-Order Nonlinear Schrödinger Equation

1State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
2School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 2 October 2014; Revised 8 December 2014; Accepted 8 December 2014

Academic Editor: Reza Jazar

Copyright © 2015 Yi Li et al. 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

The purpose of this paper is to investigate a higher-order nonlinear Schrödinger equation with non-Kerr term by using the bifurcation theory method of dynamical systems and to provide its bounded traveling wave solutions. Applying the theory, we discuss the bifurcation of phase portraits and investigate the relation between the bounded orbit of the traveling wave system and the energy level. Through the research, new traveling wave solutions are given, which include solitary wave solutions, kink wave solutions, and periodic wave solutions.