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Mathematical Problems in Engineering
Volume 2015, Article ID 310945, 7 pages
http://dx.doi.org/10.1155/2015/310945
Research Article

Exact Periodic Wave, Bisoliton, and Various Breather Solutions for the Zakharov Equations

1College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
2City and Environment College, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

Received 17 July 2015; Revised 2 November 2015; Accepted 5 November 2015

Academic Editor: Masoud Hajarian

Copyright © 2015 Heng Wang 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 Zakharov equations, which involve the interactions between Langmuir and ion acoustic waves in plasma, are analytically studied. By using the method of Exp-function, the periodic wave, bisoliton, Akhmediev breather, Ma breather, and Peregrine breather of the Zakharov equations are obtained. These results presented in this paper enrich the diversity of solution structures of the Zakharov equations. Furthermore, based on the numerical simulations of these solutions, some physics analysis of bisolitons and various breathers are given.