# On the rational solutions and the solitons of the KP hierarchy

**Date**: Friday 9 November 2018, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Seminars, Applied Mathematics, Integrable Systems**Cost**: Free

#### Yuji Kodama, Ohio State University

It is well known that the Schur polynomials give rational solutions 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 describing the most degenerate zero locus of the tau-function 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.

This work is in progress under a collaboration with A. Mikhailov and J.-P. Wang.