CLASSICAL SOLUTIONS OF THE GENERALIZED CAMASSA-HOLM EQUATION

摘要

In this paper, well-posedness in C-1(R) (a.k.a. classical solutions) for a generalized Camassa-Holm. equation (g-kbCH) having (k+1)-degree nonlinearities is shown. This result holds for the Camassa-Holm, the Degasperis-Procesi and the Novikov equations, which improves upon earlier results in Sobolev and Besov spaces.