One Step Degeneration of Trigonal Curves and Mixing of Solitons and Quasi-Periodic Solutions of the KP Equation

TL;DR

This paper studies one step degenerations of trigonal and hyperelliptic curves, analyzing their limits and revealing how solitons and quasi-periodic solutions of the KP equation can mix, using the Sato Grassmannian framework.

Contribution

It introduces a new degeneration method for trigonal and hyperelliptic curves and demonstrates the mixing of solitons with quasi-periodic solutions in the KP equation context.

Findings

Limits of quasi-periodic solutions are computed explicitly.

Mixing of solitons and quasi-periodic solutions is demonstrated.

Degeneration process reveals new solution behaviors in KP equations.

Abstract

We consider certain degenerations of trigonal curves and hyperelliptic curves, which we call one step degeneration. We compute the limits of corresponding quasi-periodic solutions using the Sato Grassmannian. The mixing of solitons and quasi-periodic solutions is clearly visible in the obtained solutions.