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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 594975, 10 pages
http://dx.doi.org/10.1155/2013/594975
Research Article

Conservation Laws of Two -Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives

Department of Mathematics, Dezhou University, Dezhou 253023, China

Received 12 May 2013; Accepted 29 June 2013

Academic Editor: Chaudry Masood Khalique

Copyright © 2013 Li-hua 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

In this paper, conservation laws for the -dimensional ANNV equation and KP-BBM equation with higher-order mixed derivatives are studied. Due to the existence of higher-order mixed derivatives, Ibragimov’s “new conservation theorem” cannot be applied to the two equations directly. We propose two modification rules which ensure that the theorem can be applied to nonlinear evolution equations with any mixed derivatives. Formulas of conservation laws for the ANNV equation and KP-BBM equation are given. Using these formulas, many nontrivial and time-dependent conservation laws for these equations are derived.