KP Solitons from Tropical Limits
Abstract of the paper: 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.
In this repository you will find the implementation of an algorithm in MAPLE for computing the truncated tau function arising from a hyperelliptic curve defined over the field \(\mathbb{Q}(\epsilon)\).
The Maple code can be viewed here:
In particular, a similar method can be used to compute the truncated tau function for a (k,n) soliton solution. Here is the Maple code for computing the truncated tau function for the (3,6) soliton soution we worked out in Example 8:
In Section 2 we list the seventeen types of Delaunay polytopes arising from metric graph of genus 4. As an example you may download the Maple code we used to calculate the Delaunay polytopes associated to the vertices of the Voronoi polytope associated to the metric graph appearing third in https://arxiv.org/abs/1707.08520, table 1:
Project page created: 5/02/2021.
Project contributors: Claudia Fevola, Daniele Agostini, Yelena Mandelshtam, and Bernd Sturmfels.
Software used: MAPLE 2019
Corresponding author of this page: Claudia Fevola, fevola@mis.mpg.de.