Infinite-peakon solutions of the Camassa-Holm equation
数学专题报告
报告题目(Title)：Infinite-peakon solutions of the Camassa-Holm equation
报告人(Speaker)：常向科 副研究员（中科院数学与系统科学研究院）
地点(Place)：后主楼1225
时间(Time)：2025年12月30日（周二）10:00-11:00
邀请人(Inviter)：孙若词、王灯山
报告摘要
We describe a class of conservative low regularity solutions to the Camassa--Holm equation on the line by exploiting the moment problem and generalized indefinite strings to develop the inverse spectral method. In particular, we identify explicitly the solutions that are amenable to this approach, which include solutions made up of infinitely many peaked solitons (peakons). As an application, our results are then used to investigate the long-time behavior of solutions. We present three exemplary cases of solutions with: (i) discrete underlying spectrum associated with zero boundary and determinate/indeterminate moment problem; (ii) step-like initial data associated with the modified Laguerre weight, and (iii) asymptotically eventually periodic initial data associated with the modified Jacobi weight.
主讲人简介
常向科，中国科学院数学与系统科学研究院副研究员、博士生导师。主要从事可积系统理论分析与数值数学等方面的研究，在重要学术刊物上发表多篇论文。获得国家优秀青年科学基金的资助，入选中国科学院青年创新促进会优秀会员。曾获得中国科学院优秀博士学位论文奖、院长奖，入选中国科学院数学与系统科学研究院“陈景润未来之星”计划等，现担任《J. Nonlinear Math. Phys.》《Phys. D》《Stud. Appl. Math.》杂志编委或青年编委等。
