JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (11): 76-85.doi: 10.6040/j.issn.1671-9352.0.2023.063

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Integrability and Birkhoff normal form of the dispersive Camassa-Holm equation

Xiaoping WU(),Gezi CHONG,Ziwen JIANG   

  1. School of Mathematics, Northwest University, Xi'an 710127, Shaanxi, China
  • Received:2023-02-27 Online:2023-11-20 Published:2023-11-07

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Abstract:

Based on the infinitely many conserved quantites of the non-dispersive Camassa-Holm equation defined on the circle, we construct the infinitely many new ones whose quadratic parts have a consistent form for the corresponding dispersive equation. As an important application, we prove that the Birkhoff normal form of any order for the dispersive Camassa-Holm equation is action-preserving.

Key words: Camassa-Holm equation, conserved quantities, action-preserving Birkhoff normal form

CLC Number: 

  • O175.29
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