This research was supported by the National Natural Science Foundation of China 11271357,11271195 and 41504078;by the CSC,the Foundation for Innovative Research Groups of the NNSFC 11321061 and the ITER-China Program 2014GB124005。
In this paper,we study the Camassa-Holm equation and the Degasperis-Procesi equation.The two equations are in the family of integrable peakon equations,and both have very rich geometric properties.Based on these geome...