KP Solitons from Tropical Limits
Algebraic Geometry
2021-05-07 v2 Mathematical Physics
math.MP
Abstract
We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann's theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota variety which parametrizes all tau functions arising from such a sum. We compute tau functions from points on the Sato Grassmannian that represent Riemann-Roch spaces and we present an algorithm that finds a soliton solution from a rational nodal curve.
Keywords
Cite
@article{arxiv.2101.10392,
title = {KP Solitons from Tropical Limits},
author = {Daniele Agostini and Claudia Fevola and Yelena Mandelshtam and Bernd Sturmfels},
journal= {arXiv preprint arXiv:2101.10392},
year = {2021}
}
Comments
21 pages, some edits based on referee comments