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Mathematical Problems in Engineering
Volume 2013, Article ID 456864, 5 pages
http://dx.doi.org/10.1155/2013/456864
Research Article

Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received 27 December 2012; Accepted 21 February 2013

Academic Editor: Farzad Khani

Copyright © 2013 Hai-Feng Zhang 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

A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of -axis and -axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.