讲座题目：On squared eigenfunction symmetries of discrete KP and mKP 主讲人：张大军 教授 主持人：傅蔚 开始时间：2019-06-25 10:30:00 结束时间：2019-06-25 11:30:00 讲座地址：中北校区数学馆东202 主办单位：计算机科学与软件工程学院
报告人简介： 张大军，上海大学数学系教授、博士生导师。主要研究领域为离散可积系统。先后主持（含完成）国家自然科学基金面上项目 5 项、教育部博士点基金 1 项、上海市项目 4 项。曾获上海市优秀博士学位论文、上海市高校优秀青年教师等。作为访问学者多次访问芬兰图尔库大学、英国利兹大学，以及澳大利亚悉尼大学等。 报告内容： We introduce a Lax triad approach to construct the scalar differential-difference Kadomtsev-Petviashvili (KP) hierarchy from a quasi-difference operator. Hamiltonian structures and symmetries of the hierarchy are discussed. The squared-eigenfunction symmetry of this hierarchy as a constraint leads the Lax triad and adjoint Lax triad of the hierarchy to a discretized AKNS spectral problem in bidirection and a semidiscrete AKNS hierarchy, which is known as the Ragnisco-Tu hierarchy. In a similar manner, it is shown that the squared-eigenfunction symmetry leads the modified differential-difference KP stuff to the relativistic Toda systems. Some new relations and reductions are found, including an one-field reduction to reduce the Ragnisco-Tu hierarchy to the Volterra hierarchy, reduction of the relativistic Toda hierarchy to the semi-discrete Burgers hierarchy which provides Bäcklund transformation of the Burgers hierarchy, and a discrete 3-point Burgers equation which is consistent around cube. |
