On the rational solutions and the solitons of the KP hierarchy

Yuji Kodama (The Ohio State University)

Thursday 11th October, 2018 16:30-17:30 Maths 110


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.

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