Geometric aspects of two- and threepeakons
arXiv:2010.02713 · doi:10.1088/1361-6544/ac149e
Abstract
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 treepeakon case) of corresponding manifolds are computed.
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