The general peakon-antipeakon solution for the Camassa-Holm equation

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 $\alpha$-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution illuminates the interplay between the various variables.