報告題目🧔🏻：可積尖峰子方程（ Integrable peakon and cuspon equations）
報告時間：2018年7月8日（周日）9⛹🏻：30--11：30
報告地點🤼：必一体育平台二樓會議室
報告人：喬誌軍🐊，美國德克薩斯大學首席教授。1997年獲得復旦大學博士學位, 師從谷超豪院士和胡和生院士。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🤞🏽。1999年獲全國百篇優秀博士論文, 1999-2001年在德國Kassel大學任Humboldt學者. 主持完成國家級和國際級項目20余項, 在《Communications in Mathematical Physics》🧑🏽、《Journal of Nonlinear Science》、《Journal of Differential Equations》等著名國際刊物發表學術論文160余篇, 出版著作2部, 組織國際會議、研討會20多次。
報告摘要🤦🏽：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 equation, constrained to a symplectic submanifold in $R^2N$, has the parametric solutions. Moreover, solving the parametric representation of the solution on the symplectic submanifold gives a class of a new algebro-geometric solution of the CH equation. In the end of my talk, some open problems are also addressed for discussion。
歡迎各位老師和同學參加🌽！