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

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  • Li-hua Zhang

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.

Suggested Citation

  • Li-hua Zhang, 2013. "Conservation Laws of Two (2+1)‐Dimensional Nonlinear Evolution Equations with Higher‐Order Mixed Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:594975
    DOI: 10.1155/2013/594975
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    References listed on IDEAS

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    1. Wazwaz, Abdul-Majid, 2008. "The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1505-1516.
    2. Dai, Chaoqing & Liu, Fengqin & Zhang, Jiefang, 2008. "Novel types of interactions between solitons in the (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov system," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 437-445.
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    Cited by:

    1. Long Wei & Yang Wang, 2014. "Comment on “Conservation Laws of Two (2 + 1)‐Dimensional Nonlinear Evolution Equations with Higher‐Order Mixed Derivatives”," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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