New construction of algebro-geometric solutions to the Camassa–Holm equation and their numerical evaluation
New construction of algebro-geometric solutions to the Camassa–Holm equation and their numerical evaluation
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DOI：
10.1098/rspa.2011.0583
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发表时间：
2011-09
期刊：
影响因子：
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通讯作者：
C. Kalla;Christian Klein
中科院分区：
文献类型：
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作者：
C. Kalla;Christian Klein
使用基于Fay恒等式的方法，给出了多维theta函数的Camassa-Holm方程的独立推导。从下伏实超椭圆曲面的拓扑结构出发，研究了这些解的真实感和光滑性条件。对具体实例的解进行了数值研究，并对表面退化为黎曼球的极限以及出现孤子和凸子的极限进行了数值研究。
An independent derivation of solutions to the Camassa–Holm equation in terms of multi-dimensional theta functions is presented using an approach based on Fay’s identities. Reality and smoothness conditions are studied for these solutions from the point of view of the topology of the underlying real hyperelliptic surface. The solutions are studied numerically for concrete examples, also in the limit where the surface degenerates to the Riemann sphere, and where solitons and cuspons appear.