報告題目：Lax integrability and the peakon problem for the modified Camass-Holm equation
中文標題：修正Camassa-Holm方程的Lax可積性與peakon問題
報告時間：2019年5月30日（周四）10：00—11：00
報告地點：必一体育平台二樓會議室
報告人：常向科副研究員，中科院系統所
報告摘要：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.