Journal of Applied Mathematics
Volume 2012 (2012), Article ID 346824, 15 pages
http://dx.doi.org/10.1155/2012/346824
Research Article

A Class of PDEs with Nonlinear Superposition Principles

Li Peng,1,2 Liu Keying,1 Pan Zuliang,3 and Zhong Weizhou2

1Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, China
2School of Economics and Finance, Xi’an Jiaotong University, Xi’an 710061, China
3Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received 29 November 2011; Revised 31 January 2012; Accepted 31 January 2012

Academic Editor: B. V. Rathish Kumar

Copyright © 2012 Li Peng 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

Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.