報告人：常向科 副研究員

報告題目：Infinite-peakon solutions of the Camassa-Holm equation

報告時間：2026年1月18日（周日）上午8：00

報告地點：云龍校區智華樓205報告廳

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

常向科，中國科學院數學與系統科學研究院副研究員，博士生導師，主要從事可積系統及相關領域的交叉研究， 部分研究成果發表在《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.》等國內外重要學術刊物上。 曾獲得中科院優秀博士學位論文獎、中科院院長獎，入選中科院青年創新促進會會員、中科院數學院“陳景潤未來之星”計劃等，并擔任《Physica D》雜志青年編委、中科院青促會數理分會會長等。

報告摘要：

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.