# 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.