Title: On the rational solutions and the solitons of the KP hierarchy
Speaker: Yuji Kodama (Ohio State University)
Abstract: It is well known that the Schur polynomials satisfy the Hirota bilinear equations of the KP hierarchy, and that each Schur polynomial can be parametrized by a unique Young diagram. We also know that the KP solitons (exponential solutions) can be parametrized by certain decomposition of the Grassmannians. In the talk, I will explain the connection between the rational solutions and the KP solitons in terms of the Young diagrams. More explicitly, I will show how one gets a rational solution from a KP soliton. I will also discuss a connection between quasi-periodic solutions (theta or sigma functions) and the KP solitons. The rational solutions then give theta divisors of certain algebraic curves. The talk will be an elementary introduction of the Sato theory of the KP hierarchy.
Seminar URL: https://research.math.osu.edu/gcis/
