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Mathematical Problems in Engineering
Volume 2015, Article ID 426363, 10 pages
http://dx.doi.org/10.1155/2015/426363
Research Article

Lie Symmetry Analysis and New Exact Solutions for a Higher-Dimensional Shallow Water Wave Equation

Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 10 May 2015; Accepted 21 June 2015

Academic Editor: Chaudry Masood Khalique

Copyright © 2015 Yinghui He. 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

In our work, a higher-dimensional shallow water wave equation, which can be reduced to the potential KdV equation, is discussed. By using the Lie symmetry analysis, all of the geometric vector fields of the equation are obtained; the symmetry reductions are also presented. Some new nonlinear wave solutions, involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. Our work extends pioneer results.