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        喬志軍: Integrable systems with peakons and cuspons, 7月6日 上午 10:00, L1218
        2019-07-05 10:40  



        Abstract: In my talk, I will introduce integrable peakon and cuspon equations and present a basic approach how to get peakon solutions. Those equations include the well-known Camassa-Holm (CH), the Degasperis-Procesi (DP), and other new peakon equations with M/W-shape solutions. I take the CH case as a typical example to explain the details. My presentation is based on my previous work (Communications in Mathematical Physics 239, 309-341). I will show that the Camassa-Holm (CH) spectral problem yields two different integrable hierarchies of nonlinear evolution equations (NLEEs), one is of negative order CH hierarchy while the other one is of positive order CH hierarchy. The two CH hierarchies possess the zero curvature representations through solving a key matrix equation. We see that the well-known CH equation is included in the negative order CH hierarchy while the Dym type equation is included in the positive order CH hierarchy. In particular, the CH peakon equation is extended to the FORQ and other higher order peakon models with peakon and weak-kink solutions. In the end of my talk, some open problems are also addressed for discussion.


        喬志軍教授于1997年獲得復旦大學數學系博士學位,從師谷超豪院士和胡和生院士。1999年獲得百篇優秀博士畢業論文。1997-2001任遼寧大學數學系教授。1999-2001,德國洪堡基金獲得者?,F任美國德克薩斯大學數學學院講席教授?,F有40多位海外專家合作者, 已經指導5位博士后及超過20位研究生。研究方向是非線性偏微分方程,可積系統與非線性尖孤波,KdV方程和孤立子理論,可積辛映射,R-矩陣理論,雷達圖像處理和數學物理的反問題?,F已出版著作2部,發表論文180余篇,其中包括著名國際雜志《數學物理學通訊》、《非線性科學》等?,F作為項目負責人已經完成20多個國家項目。組織超過20個國際會議、研討會。任國際期刊《Journal of Applied Analysis and Computation》和《Advances in Mathematical Physics》編委

        Three Gorges Math Research Center  443002, Yichang, Hubei