题目:Lattice Boussinesq equations as reductions of bilinear lattice KP and mKP equations

报告人:  田可雷 副教授

        合肥工业大学数学系

时间: 2015年1月8日  下午4:30—5:30

地点: 科大东区管理科研楼1518教室

An elegant and comprehensive theory of soliton equations is provided by the Sato theory, developed by Mikio Sato and his school in Kyoto. This theory contains many interesting mathematical structures and in particular provides the construction of hierarchies of soliton equations, written in terms of tau-functions depending on infinite number of independent variables. One aspect of this approach is the coding of hierarchies of equations, their Lax pairs,and soliton solutions into compact bilinear identities. What is remarkable (and essential for our approach) is that although the theory was originally developed to continuous PDEs it can be easily transformed into discrete PDEs by using Miwa’s transform. Examples of this were presented by Date, Jimbo and Miwa in a series of papers.

In this talk we will elaborate  the reduction process by which one gets lower dimensional discrete equations from fully discrete 3D master equations, which we take to be either KP or 1st modified KP equations. We consider in particular the reductions that lead to discrete versions of the Boussinesq equation (BSQ).

欢迎广大师生参加！