New construction of algebro-geometric solutions to the Camassa-Holm   equation and their numerical evaluation
  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. 
C. Kalla, C. Klein
math-ph math.MP nlin.SI