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中文摘要：
近20年来,浅水波模型Camassa-Holm（CH）方程受到诸多研究者关注.在之前的工作中,通过Hirota双线性方法得到了CH方程的单周期解.基于此,该文将对N=2时CH方程的拟周期解及其渐近行为进行研究.首先,回顾了坐标变换,扩展的双线性形式和Riemann（黎曼）θ-函数等内容,并在此基础上利用Hirota双线性方法构造了在N=2时CH方程含有多个参数的拟周期解,并且该拟周期解是由Riemannθ-函数表示的.其次,发现了该拟周期解渐近行为的一个特点,即CH方程的此拟周期解可以退化为其2孤子解.
英文摘要：
Many researchers have paid attention to the shallow water wave model Camassa- Holm （CH） equation over the last 2 decades. The single periodic solution to the CH equation based on the Hirota bilinear method had been presented in our previous work. The quasi-period- ic solution in genus 2 and its asymptotic behavior were given. First, the parameters appearing in the bilinear equation system were rearranged, such as the coordinate transformation, the ex- tended bilinear form, the Riemman theta function and so on. Then the quasi-periodic solution to the CH equation was obtained, which was expressed in the form of the Riemann theta function in genus 2. Second, the asymptotic behavior of the quasi-periodic solution was discussed. It is shown that this solution can degenerate into the CH equation＇ s 2-soliton solution.
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