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Global Conservative and Multipeakon Conservative Solutions for the Modified Camassa-Holm System with Coupling Effects

机译：具有耦合效应的改进的Camassa-Holm系统的全局守恒和多峰守恒解

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摘要

This paper investigates the continuation of solutions to the modified coupled two-component Camassa-Holm system after wave breaking. The underlying problem is rather challenging due to the mutual coupling effect between two components in the system. By introducing a novel transformation that makes use of a skillfully defined characteristic and a set of newly defined variables, the original system is converted into a Lagrangian equivalent system, from which the global conservative solution is obtained, which further allows for the establishment of the multipeakon conservative solution of the system. The results obtained herein are deemed useful for understanding the inevitable phenomenon near wave breaking.
机译：本文研究了破波后改进的耦合双组分Camassa-Holm系统解的连续性。由于系统中两个组件之间的相互耦合作用，潜在的问题颇具挑战性。通过引入利用熟练定义的特征和一组新定义的变量的新颖变换，将原始系统转换为拉格朗日等效系统，从中获得全局保守解，进而允许建立多峰系统的保守解决方案。本文获得的结果被认为对于理解近波破碎的不可避免现象是有用的。

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  • 来源
    《Mathematical Problems in Engineering》 |2014年第8期|606249.1-606249.17|共17页
  • 作者

    Huabin Wen; Yujuan Wang; Yongduan Song; Hamid Reza Karimi;

  • 作者单位

    School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China;

    School of Automation, Chongqing University, Chongqing 400044, China;

    School of Automation, Chongqing University, Chongqing 400044, China;

    Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway;

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