Space Curves and Solitons of the KP Hierarchy
发布时间：2021年04月26日
浏览次数：5523
发布者: He Liu
主讲人： Yuancheng Xie (Ohio State University)
活动时间： 从 2021-04-27 16:00 到 17:00
场地： 北京国际数学研究中心，全斋全29教室
It is well known that algebro-geometric solutions of the KdV hierarchy are constructed from the Riemann theta (or Klein sigma) functions associated with hyperelliptic curves, and soliton solutions can be obtained by rational limits of the corresponding curves.
In this talk, I will associate a class of KP solitons with a family of singular space curves indexed by the numerical semigroups $\langle l, lm+1, \dots, lm+k \rangle$ where $m \ge 1$ and $1 \le k \le l-1$. Some of these curves can be deformed into smooth "space curves", and they provide canonical models for the $l$-th generalized KdV hierarchies (KdV hierarchy corresponds to the case $l = 2$). If time permits, we will also see how to construct the space curves from a commutative ring of differential operators in the sense of the well-known Burchnall-Chaundy theory.
This is a joint work with Yuji Kodama.
