报告人：Prof. Folkert Müller-Hoissen

单位：德国哥廷根大学理论物理研究所、德国马克斯普朗克研究所

时间：2019年10月15日（周二）10:00-11:00

地点：长安校区东学楼二层 非线性科学研究中心报告厅（0227）

报告摘要：The Korteweg-deVries (KdV) equation is a prime example of a "soliton equation", a partial differential (or difference) equation possessing exact solutions of which an arbitrary number can be superposed in a nonlinear way. For KdV, these solutions are waves exponentially localized in the spatial dimension and exhibit only a spatial displacement due to their interaction. For a matrix version of KdV, solitons carry "internal" degrees of freedom, which we call polarizations, and there is more happening when they interact. The 2-soliton solution determines a map of two "incoming" to two "outgoing" polarizations (where "in" and "out" refer to large negative, respectively positive values of time). This map turned out to be a solution of the set-theoretical Yang-Baxter equation, a "Yang-Baxter map" for short (Veselov 2004), which is actually a statement about the interaction of three solitons. Whereas polarizations can be assigned to solitons asymptotically (for large negative and large positive times), when they get closer together they merge as waves and loose their identity. However, taking the "tropical limit" of a soliton solution reveals their identity and we can follow the evolution of polarizations for all times. The tropical limit of a soliton solution of an equation like KdV or Boussinesq, for example, consists of a planar, piecewise linear graph, together with polarizations along its segments. But in case of the Boussinesq equation, a Yang-Baxter map is no longer sufficient to describe the evolution of polarizations along a tropical limit graph, though it works for a subclass of solutions.

In this talk we will report, more generally, on corresponding insights for the KP equation, which generalizes KdV to three dimensions, and the two-dimensional Toda lattice equation.

报告人简介：Folkert Müller-Hoissen教授目前工作于德国哥廷根大学理论物理研究所和德国马克斯普朗克研究所，是国际上可积系统和广义相对论、理论物理领域的著名学者。

望各位老师和同学踊跃参加！