报告人：常向科 副研究员
报告题目：Infinite-peakon solutions of the Camassa-Holm equation
报告时间：2026年1月18日（周日）上午8：00
报告地点：云龙校区智华楼205报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
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，主要从事可积系统及相关领域的交叉研究， 部分研究成果发表在《Adv. Math.》、《Commun. Math. Phys.》、《Int. Math. Res. Not.》、《J. Differ. Equations》、《J. Nonlinear Sci.》、《Nonlinearity》、《Numer. Math.》、《Sci. China Inform. Sci.》、《Sci. China Math.》、《SIAM J. Discrete Math.》、《Stud. Appl. Math.》等国内外重要学术刊物上。 曾获得中科院优秀博士学位论文奖、中科院院长奖，入选中科院青年创新促进会会员、中科院数学院“陈景润未来之星”计划等，并担任《Physica D》杂志青年编委、中科院青促会数理分会会长等。
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 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.
