6533b834fe1ef96bd129d67d
RESEARCH PRODUCT
New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation
Caroline KallaChristian Kleinsubject
Surface (mathematics)General MathematicsFOS: Physical sciencesGeneral Physics and AstronomyRiemann sphereTheta function01 natural sciences010305 fluids & plasmassymbols.namesake[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesLimit (mathematics)0101 mathematics[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Shallow water equationsNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsMathematicsSmoothnessCamassa–Holm equationNonlinear Sciences - Exactly Solvable and Integrable Systems010102 general mathematicsMathematical analysisGeneral Engineering[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Mathematical Physics (math-ph)Nonlinear Sciences::Exactly Solvable and Integrable SystemssymbolsExactly Solvable and Integrable Systems (nlin.SI)Hyperelliptic surfacedescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-28 | Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 468 (2012), no. 2141, 1371–1390 |