Higher Dimensional Camassa–Holm Equations

Utilizing some conservation laws of the (1+1)-dimensional Camassa–Holm (CH) equation and/or its reciprocal forms, some (n+1)-dimensional CH equations for n ≥ 1 are constructed by a modified deformation algorithm. The Lax integrability can be proven by applying the same deformation algorithm to the L...

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Bibliographic Details
Published in:Chinese physics letters 2023-02, Vol.40 (2), p.20201-5
Main Authors: Lou, S. Y., Jia, Man, Hao, Xia-Zhi
Format: Article
Language:English
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Summary:Utilizing some conservation laws of the (1+1)-dimensional Camassa–Holm (CH) equation and/or its reciprocal forms, some (n+1)-dimensional CH equations for n ≥ 1 are constructed by a modified deformation algorithm. The Lax integrability can be proven by applying the same deformation algorithm to the Lax pair of the (1+1)-dimensional CH equation. A novel type of peakon solution is implicitly given and expressed by the LambertW function.
ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307X/40/2/020201