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| 摘要: |
| 本文研究了广义的高阶Camassa-Holm类方程, 简记为ghmCH方程. 在$s > \frac{7}{2}$, 初值 $u_{0}$ 属于$H^{s}(\mathbb{R} )$ 的条件下, 我们建立了该方程的局部适定性. 除此之外, 我们获得了该方程的弱形式, 并证明了单峰解和多峰动力系统的存在性. |
| 关键词: 广义的高阶Camassa-Holm类方程 局部适定性 尖峰孤子解 |
| DOI： |
| 分类号:35A01; 35C08; 35D30; 35G25 |
| 基金项目: |
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| WELL-POSEDNESS AND PEAKON SOLUTIONS FOR A HIGHER ORDER CAMASSA-HOLM TYPE EQUATION |
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chenshuang
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| Abstract: |
| In this paper, we delve into a generalized higher order Camassa-Holm type equation, (or, an ghmCH equation for short). We establish local well-posedness for this equation under the condition that the initial data $u_{0}$ belongs to the Sobolev space $H^{s}(\mathbb{R} )$ for some $s>\frac{7}{2}$. In addition, we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system. |
| Key words: Generalized higher order Camassa-Holm type equation Local well-posedness Peakon |
