Peakons of the Camassa-Holm equation

摘要

From the mathematical point of view, we use the bifurcation method of phase plane to study the CH equation given by Camassa and Holm [Phys. Rev. Lett. 71 (11)(1993) 1661]. In case of k=0, they showed that it has solitary waves of the form ce~-|x-ct|, which were called "peakons". When k ≠0, we obtain the peakons of the form (3k/2) exp(-x-(kt/2))-k in three different ways, which are also applicable to the case of k=0. Note that our approaches and also be used to study the traveling waves in various nonlinear in- tegrable equations.