Preprint 2015-005
The general peakon-antipeakon solution for the Camassa–Holm equation
Katrin Grunert and Helge Holden
Abstract: We compute explicitly the peakon-antipeakon solution of the Camassa–Holm equation $u_t−u_{txx}+3uu_x−2u_xu{xx}−uu_{xxx}=0$ in the non-symmetric and $α$-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution illuminates the interplay between the various variables.