KP solitons and the Schottky uniformization
Exactly Solvable and Integrable Systems
2025-10-08 v2 Mathematical Physics
Algebraic Geometry
Combinatorics
math.MP
Abstract
Real and regular soliton solutions of the KP hierarchy have been classified in terms of the totally nonnegative (TNN) Grassmannians. These solitons are referred to as KP solitons, and they are expressed as singular (tropical) limits of shifted Riemann theta functions. In this talk, for each element of the TNN Grassmannian, we construct a Schottky group, which uniformizes the Riemann surface associated with a real finite-gap solution. Then we show that the KP solitons are obtained by degenerating these finite-gap solutions.
Keywords
Cite
@article{arxiv.2507.20296,
title = {KP solitons and the Schottky uniformization},
author = {Takashi Ichikawa and Yuji Kodama},
journal= {arXiv preprint arXiv:2507.20296},
year = {2025}
}
Comments
Up-dated by expanding the previous version for "Talk at the meeting of Japanese Mathematical Society on September 16-19, 2025"