Abstract and Applied Analysis

Conservation Laws of Two ( 2 + 1 ) -Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives

Li-hua Zhang

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Abstract

In this paper, conservation laws for the ( 2 + 1 ) -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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 594975, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449900

Digital Object Identifier
doi:10.1155/2013/594975

Mathematical Reviews number (MathSciNet)
MR3124073

Zentralblatt MATH identifier
07095149

Citation

Zhang, Li-hua. Conservation Laws of Two $(2+1)$ -Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 594975, 10 pages. doi:10.1155/2013/594975. https://projecteuclid.org/euclid.aaa/1393449900


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