Lax integrability and the peakon problem for the modified Camass-Holm equation
报告人:常向科博士,中国科学院数学与系统科学研究院 时间:2019年06月19日(周三)上午9:00
摘要:Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. In this talk, we give a complete construction of peakon solutions satisfying the modified Camassa-Holm (or called FORQ)  equation in the sense of distributions; our approach is based on solving certain inverse boundary value problem the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Pad\'{e} approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons which share asymptotic speeds, as well as Toda-like sorting property.