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数学学术报告:From discrete integrable system to continuous integrable system
2019-06-14 | 编辑: | 【  】【打印】【关闭

   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.

  欢迎参加!








 
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