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Symmetries and their lie algebra of a variable coefficient Korteweg-de Vries hierarchy

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Abstract

Isospectral and non-isospectral hierarchies related to a variable coefficient Painlevé integrable Korteweg-de Vries (KdV for short) equation are derived. The hierarchies share a formal recursion operator which is not a rigorous recursion operator and contains t explicitly. By the hereditary strong symmetry property of the formal recursion operator, the authors construct two sets of symmetries and their Lie algebra for the isospectral variable coefficient Korteweg-de Vries (vcKdV for short) hierarchy.

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Authors and Affiliations

  1. College of Sciences, Shandongjianzhu University, Jinan, 250101, China

    Xiaoying Zhu

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Dajun Zhang

Authors
  1. Xiaoying Zhu
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  2. Dajun Zhang
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Correspondence to Xiaoying Zhu.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11071157) and Doctor of Campus Foundation of Shandongjianzhu University (No. 1275).

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Zhu, X., Zhang, D. Symmetries and their lie algebra of a variable coefficient Korteweg-de Vries hierarchy. Chin. Ann. Math. Ser. B 37, 543–552 (2016). https://doi.org/10.1007/s11401-016-1020-2

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  • DOI: https://doi.org/10.1007/s11401-016-1020-2

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