Qualitative Analysis for a New Integrable Two-Component Camassa–Holm System with Peakon and Weak Kink Solutions
Qualitative Analysis for a New Integrable Two-Component Camassa–Holm System with Peakon and Weak Kink Solutions
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DOI：
10.1007/s00220-014-2236-1
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发表时间：
2014-12
影响因子：
2.4
通讯作者：
Kai Yan;Z. Qiao;Z. Yin
中科院分区：
文献类型：
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作者：
Kai Yan;Z. Qiao;Z. Yin
本文研究了一类新的具有峰值孤子和弱扭结解的可积两分量Camassa-Holm系统。它是第一个具有弱扭结和扭结-峰子干涉解的可积系统。此外，新系统包括标准（二次）和三次Camassa-Holm方程作为两种特殊情况。本文首先建立了系统Cauchy问题的局部适定性，然后给出了具有二次和三次非线性项的系统强解的精确爆破情形和一个新的爆破结果.此外，还讨论了它的峰子解和弱扭结解。
This paper is devoted to a new integrable two-component Camassa–Holm system with peaked solitons (peakons) and weak-kink solutions. It is the first integrable system that admits weak kink and kink–peakon interactional solutions. In addition, the new system includes both standard (quadratic) and cubic Camassa–Holm equations as two special cases. In the paper, we first establish the local well-posedness for the Cauchy problem of the system, and then derive a precise blow-up scenario and a new blow-up result for strong solutions to the system with both quadratic and cubic nonlinearity. Furthermore, its peakon and weak kink solutions are discussed as well.