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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 > 7/2,初值u0属于Hs(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:O175.2 |
| 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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CHEN shuang
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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 u0 belongs to the Sobolev space Hs(R) for some s > 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 |
