数学学术报告：From discrete integrable system to continuous integrable system
来源： 时间：2019-06-14
报告题目: From discrete integrable system to continuous integrable system 报 告 人： 冯宝峰教授（Baofeng Feng，University of Texas Rio Gande Valley） 报告时间：2019年6月19日（周三）10：00-11：00 报告地点：新波谱楼12楼1217报告厅
摘要：In this talk, I will give a review on recent development of integrable system, especially the discrete inegrable system. It is known that the tau-functions play a crucial role in both the continuous and discrete integrable sytems. We will start with a type of Gam determinant solution and show it satisfies the Hirota-Miwa equation, or the discrete Kadomtsev-Petviashvili (KP) equation. By introducing Schur polynomial, and Miwa transformation, we will derive the KP hierarchy, whose reductions give rise to the Korteweg-de Vries (KdV) equation and Boussinesq equation. Then we will show by simple transformations, the discrete KP equation can be transformed into discrete modified KP equation and the discrete KP-Toda lattice equation, which in turn lead to the modified KP and KP-Toda hierarchy, whose reductions give the modified KdV equation and Sine-Gordon equation, respectively.
讲座预告
数学学术报告：From discrete integrable system to continuous integrable system
报告题目: From discrete integrable system to continuous integrable system
报 告 人： 冯宝峰教授（Baofeng Feng，University of Texas Rio Gande Valley）
报告时间：2019年6月19日（周三）10：00-11：00
报告地点：新波谱楼12楼1217报告厅
摘要：In this talk, I will give a review on recent development of integrable system, especially the discrete inegrable system. It is known that the tau-functions play a crucial role in both the continuous and discrete integrable sytems. We will start with a type of Gam determinant solution and show it satisfies the Hirota-Miwa equation, or the discrete Kadomtsev-Petviashvili (KP) equation. By introducing Schur polynomial, and Miwa transformation, we will derive the KP hierarchy, whose reductions give rise to the Korteweg-de Vries (KdV) equation and Boussinesq equation. Then we will show by simple transformations, the discrete KP equation can be transformed into discrete modified KP equation and the discrete KP-Toda lattice equation, which in turn lead to the modified KP and KP-Toda hierarchy, whose reductions give the modified KdV equation and Sine-Gordon equation, respectively.
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