Asymptotic Stability for Some Non positive Perturbations of the Camassa–Holm Peakon with Application to the Antipeakon–peakon Profile. (2nd October 2018) - Molinet, Luc
Abstract: We continue our investigation on the asymptotic stability of the peakon. In a 1st step we extend our asymptotic stability result [30 ] in the class of functions whose negative part of the momentum density is supported in ]-∞, x_0] and the positive part in [x_0, +∞ [ for some x_0R . In a 2nd step this enables us to prove the asymptotic stability of well-ordered train of antipeakons–peakons and, in particular, of the antipeakon–peakon profile. Finally, in the appendix we prove that in the case of a nonnegative momentum density the energy at the left of any given point decays to zero as time goes to +∞ . This leads to an improvement of the asymptotic stability result stated in [30 ].