報(bào)告人：常向科 副研究員
報(bào)告題目：Infinite-peakon solutions of the Camassa-Holm equation
報(bào)告時(shí)間：2026年1月18日（周日）上午8：00
報(bào)告地點(diǎn)：云龍校區(qū)智華樓205報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
常向科，中國(guó)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(guó)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(jiǎng)、中科院院長(zhǎng)獎(jiǎng)，入選中科院青年創(chuàng)新促進(jìn)會(huì)會(huì)員、中科院數(shù)學(xué)院“陳景潤(rùn)未來之星”計(jì)劃等，并擔(dān)任《Physica D》雜志青年編委、中科院青促會(huì)數(shù)理分會(huì)會(huì)長(zhǎng)等。
報(bào)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.