Properties Of Solutions Near The Peakons Of The Degasperis-Procesi Eqaution

This paper studies the orbital stability of peakon for the Degasperis-Procesi equation and the blow-up of solution near the peakon for Cauchy problem of the Degasperis-Procesi equation.By the extended pseudo-conformal transformation method,the solution near the peakon for Degasperis-Procesi equation is decomposed as follows:?1/2(t)u(t,y+x(t))=Q(y)+?(t,y),and the L2 stability of the residual is studied via the parameter modulation theory,consequently,we prove the orbital stability of peakon for the Degasperis-Procesi equation in the L2 normOn the basis of decomposition,the blow-up of solution near the peakon for Degasperis-Procesi equation is studied,a sufficient condition for the existence of blow-up solution and the blow-up rate are obtained,moreover,the relationship between blow-up of solution and blow-up of residual are studied and it is obtained that blow-up of solution and blow-up of residual are equivalent.