报告主题：修正Camass-Holm方程的Lax可积性与尖峰孤子
报告人：常向科 副研究员（中国科学院）
报告时间：2019年3月4日（周一）14:00-15:30
报告地点：校本部G507
邀请人：张大军
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.
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