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(diǎn)：云龍校區(qū)智華樓205報告廳

主辦單位：數(shù)學(xué)與統(tǒng)計學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報告人簡介：

常向科，中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院副研究員，博士生導(dǎo)師，主要從事可積系統(tǒng)及相關(guān)領(lǐng)域的交叉研究， 部分研究成果發(fā)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(nèi)外重要學(xué)術(shù)刊物上。 曾獲得中科院優(yōu)秀博士學(xué)位論文獎、中科院院長獎，入選中科院青年創(chuàng)新促進(jìn)會會員、中科院數(shù)學(xué)院“陳景潤未來之星”計劃等，并擔(dān)任《Physica D》雜志青年編委、中科院青促會數(shù)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.