报告题目：Lax integrability and the peakon problem for the modified Camass-Holm equation
中文标题：修正Camassa-Holm方程的Lax可积性与peakon问题
报告时间：2019年5月30日（周四）10：00—11：00
报告地点：开云·电竞(中国)官方网站二楼会议室
报告人：常向科副研究员，中科院系统所
报告摘要：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.