Moment modification, multipeakons, and nonisospectral generalizations

Xiang-Ke Chang Xing-Biao Hu Shi-Hao Li

Dynamical Systems mathscidoc:1912.43176

Journal of Differential Equations, 265, (9), 3858-3887, 2018.11
Firstly, a formal correspondence is established between the CamassaHolm (CH) equation and a two-component modified CH (or called SQQ) equation according to the method of <i>moment modification</i> for multipeakon formulae. Secondly, based on the generalized nonisospectral CH equation in Chang et al. (2014) [14] and the interlacing multipeakons of the two-component modified CH equation in Chang et al. (2016) [15], we propose a new generalized two-component modified CH equation with two parameters, which possesses a nonisospectral Lax pair. The proposed equation still admits multipeakon solutions of explicit and closed form. Sufficient conditions for global existence of solutions are given and two concrete examples with certain interesting phenomenon are presented. Last of all, as a by-product, a generalized nonisospectral modified CH equation is deduced, together with its Lax pair.
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@inproceedings{xiang-ke2018moment,
  title={Moment modification, multipeakons, and nonisospectral generalizations},
  author={Xiang-Ke Chang, Xing-Biao Hu, and Shi-Hao Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112738825652736},
  booktitle={Journal of Differential Equations},
  volume={265},
  number={9},
  pages={3858-3887},
  year={2018},
}
Xiang-Ke Chang, Xing-Biao Hu, and Shi-Hao Li. Moment modification, multipeakons, and nonisospectral generalizations. 2018. Vol. 265. In Journal of Differential Equations. pp.3858-3887. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112738825652736.
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