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

Author

Listed:
  • Long Wei
  • Yang Wang

Abstract

In a recent paper (Zhang (2013)), the author claims that he has proposed two rules to modify Ibragimov’s theorem on conservation laws to “ensure the theorem can be applied to nonlinear evolution equations with any mixed derivatives.” In this letter, we analysis the paper. Indeed, the so‐called “modification rules” are needless and the theorem of Ibragimov can be applied to construct conservation laws directly for nonlinear equations with any mixed derivatives as long as the formal Lagrangian is rewritten in symmetric form. Moreover, the conservation laws obtained by the so‐called “modification rules” in the paper under discussion are equivalent to the one obtained by Ibragimov’s theorem.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:264049
    DOI: 10.1155/2014/264049
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    References listed on IDEAS

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    1. Li-hua Zhang, 2013. "Conservation Laws of Two -Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    2. 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).
    3. Yang Wang & Long Wei, 2013. "Self‐Adjointness, Symmetries, and Conservation Laws for a Class of Wave Equations Incorporating Dissipation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Yang Wang & Long Wei, 2013. "Self-Adjointness, Symmetries, and Conservation Laws for a Class of Wave Equations Incorporating Dissipation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, May.
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