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Advances in Mathematical Physics
Volume 2014, Article ID 974050, 8 pages
http://dx.doi.org/10.1155/2014/974050
Research Article

Separation Transformation and a Class of Exact Solutions to the Higher-Dimensional Klein-Gordon-Zakharov Equation

1School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China
2School of Science, Beijing Information Science and Technology University, Beijing 100192, China
3China Petroleum Engineering and Construction Corp., Beijing 100028, China

Received 8 February 2014; Accepted 30 March 2014; Published 24 April 2014

Academic Editor: Christian Maes

Copyright © 2014 Jing Chen 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 separation transformation method is extended to the -dimensional Klein-Gordon-Zakharov equation describing the interaction of the Langmuir wave and the ion acoustic wave in plasma. We first reduce the -dimensional Klein-Gordon-Zakharov equation to a set of partial differential equations and two nonlinear ordinary differential equations of the separation variables. Then the general solutions of the set of partial differential equations are given and the two nonlinear ordinary differential equations are solved by extended -expansion method. Finally, some new exact solutions of the -dimensional Klein-Gordon-Zakharov equation are proposed explicitly by combining the separation transformation with the exact solutions of the separation variables. It is shown that, for the case of , there is an arbitrary function in every exact solution, which may reveal more nontrivial nonlinear structures in the high-dimensional Klein-Gordon-Zakharov equation.