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Comment on: ``Conservation laws of two \((2+1)\)-dimensional nonlinear evolution equations with higher-order mixed derivatives'' (Q1722501)

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scientific article; zbMATH DE number 7022045
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Comment on: ``Conservation laws of two \((2+1)\)-dimensional nonlinear evolution equations with higher-order mixed derivatives''
scientific article; zbMATH DE number 7022045

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    Comment on: ``Conservation laws of two \((2+1)\)-dimensional nonlinear evolution equations with higher-order mixed derivatives'' (English)
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    14 February 2019
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    Summary: In a recent paper [``Conservation laws of two \((2+1)\)-dimensional nonlinear evolution equations with higher-order mixed derivatives'', ibid. 2013, Article ID 594975, 10 p. (2013; Zbl 1432.35190), see \url{doi:10.1155/2013/594975}], \textit{L.-H. Zhang} 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.
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    needless modification rules
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