色散Camassa-Holm方程的可积性及Birkhoff规范型  

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

作　　者：吴孝平 种鸽子 姜自文 WU Xiaoping;CHONG Gezi;JIANG Ziwen(School of Mathematics,Northwest University,Xi'an 710127,Shaanxi,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《山东大学学报（理学版）》2023年第11期76-85,共10页Journal of Shandong University(Natural Science)

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。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.

关 键 词：CAMASSA-HOLM方程 守恒量 保作用量的Birkhoff规范型 

分 类 号：O175.29[理学—数学]