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

Paper:
Available as PDF (477 Kbytes).
Author(s):
Katrin Grunert,
Helge Holden,
Submitted by:
; 2015-02-26.