Moment modification, multipeakons, and nonisospectral generalizations
Moment modification, multipeakons, and nonisospectral generalizations
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矩修正、多峰值和非等谱概括
DOI：
10.1016/j.jde.2018.05.020
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发表时间：
2018
影响因子：
2.4
通讯作者：
Shi Hao Li
中科院分区：
文献类型：
--
作者：
Xiang Ke Chang;Xing Biao Hu;Shi Hao Li
首先，根据多峰公式的矩修正方法，建立了Camassa-Holm(CH)方程和一个二分量修正的CH(或称为SQQ)方程之间的形式对应。其次，基于Chang等人的广义非等谱CH方程。(2014)[14]和Chang等人提出的二分量修正CH方程的交错多峰。在(2016)[15]的基础上，我们提出了一个新的具有非等谱Lax对的两参数广义两分量修正CH方程。所提出的方程仍然允许显式和闭式的多峰解。给出了整体解存在的充分条件，并给出了两个具有某些有趣现象的具体例子。最后，作为副产品，导出了一个广义非等谱修正的CH方程及其Lax对。
Firstly, a formal correspondence is established between the Camassa–Holm (CH) equation and a two-component modified CH (or called SQQ) equation according to the method ofmoment modificationfor 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.