New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation

Details 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

2011-09-24

arxiv.org/abs/1109.5301v2

Physics

Mathematical Physics

19 pages, 9 figures

Scientific paper

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.

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