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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 348796, 7 pages
http://dx.doi.org/10.1155/2014/348796
Research Article

Soliton and Breather Solutions for the Mixed Nonlinear Schrödinger Equation via -Fold Darboux Transformation

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

Received 19 February 2014; Accepted 29 April 2014; Published 21 May 2014

Academic Editor: Abdul Hamid Kara

Copyright © 2014 Hui-Qin Hao 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

Under investigation in this paper is the mixed nonlinear Schrödinger equation, which describes the propagation of the subpicosecond or femtosecond optical pulse in a monomodal optical fiber. The Darboux transformation is constructed and -times iterative potential formula is presented. Two-soliton and breather solutions are derived on the vanishing and two types of nonvanishing backgrounds: the continuous wave(cw) background and constant background, respectively. The dynamic features of the solitons and breathers are discussed via analytic solutions and graphical illustration.