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

Caroline Kalla (1) , Christian Klein (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Domaines: Physique mathématique [math-ph]

Caroline Kalla, Christian Klein. New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation. 2011. ⟨hal-00627156⟩