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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (11): 76-85.doi: 10.6040/j.issn.1671-9352.0.2023.063

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色散Camassa-Holm方程的可积性及Birkhoff规范型

吴孝平(),种鸽子,姜自文   

  1. 西北大学数学学院, 陕西 西安 710127
  • 收稿日期:2023-02-27 出版日期:2023-11-20 发布日期:2023-11-07
  • 作者简介:吴孝平(1984—)，女，讲师，博士，研究方向为偏微分方程的KAM理论. E-mail：506159177@qq.com

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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摘要：

基于已知的单位圆周上的非色散Camassa-Holm方程的无穷多守恒律, 构造出相应色散方程且新的二次项具有统一形式的无穷多守恒律。作为其重要应用, 证明了色散Camassa-Holm方程任意阶的Birkhoff规范型是保作用量的。

关键词: Camassa-Holm方程, 守恒量, 保作用量的Birkhoff规范型

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

中图分类号: 

  • O175.29
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