A rigidity result for the Holm–Staley b-family of equations with application to the asymptotic stability of the Degasperis–Procesi peakon. (December 2019) - Molinet, Luc
Abstract: We prove that the peakons are asymptotically stable, under the flow of the Degasperis–Procesi equation, in the class of functions with a momentum density that belongs to M + ( R ) . The key argument is a rigidity result for uniformly in time exponentially decaying global solutions that is shared by the Holm–Staley b -family of equations for b ≥ 1 . This extends previous results obtained for the Camassa–Holm equation ( b = 2 ).