Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 925187, 5 pages
doi:10.1155/2009/925187
Research Article

Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

Weimin Zhang1,2

1Department of Mathematics, Jiaying University, Meizhou, Guangdong 514015, China
2Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 4 February 2009; Accepted 7 March 2009

Academic Editor: Ji Huan He

Copyright © 2009 Weimin Zhang. 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

Variational principles for nonlinear partial differential equations have come to play an important role in mathematics and physics. However, it is well known that not every nonlinear partial differential equation admits a variational formula. In this paper, He's semi-inverse method is used to construct a family of variational principles for the long water-wave problem.