Geometric aspects of two- and threepeakons

We apply geometric tools to study dynamics of two- and threepeakon solutions of the Camassa-Holm equation. New proofs of asymptotic behavior of the solutions are given. In particular we recover well-known collision conditions. Additionally the Gauss curvature (in the twopeakon case) and the sectional curvature (in the threepeakon case) of corresponding manifolds are computed.

Automated summary

Geometric tools were applied to study the dynamics of two- and three-peakon solutions of the Camassa-Holm equation. New proofs of the solutions' asymptotic behavior were provided, recovering well-known collision conditions. Additionally, the Gauss curvature (in the two-peakon case) and sectional curvature (in the three-peakon case) of corresponding manifolds were computed.