Comment on “Conservation Laws of Two (2 + 1)-Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives”
Comment on “Conservation Laws of Two (2 + 1)-Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives”
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DOI：
10.1155/2014/264049
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发表时间：
2014-01
影响因子：
--
通讯作者：
Long Wei;Yang Wang
中科院分区：
文献类型：
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作者：
Long Wei;Yang Wang
在最近的一篇论文（Zhang(2013)）中，作者声称他提出了两条规则来修改Ibragimov关于守恒定律的定理，以“确保该定理可以应用于任何混合导数的非线性演化方程”。在这封信中，我们对论文进行了分析。实际上，所谓的“修正规则”是不必要的，只要将形式拉格朗日量改写为对称形式，Ibragimov定理就可以直接用于构造具有任何混合导数的非线性方程的守恒律。此外，本文所讨论的所谓“修正规则”所得到的守恒定律与伊布拉吉莫夫定理所得到的守恒定律是等价的。
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.