Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs
Exactly Solvable and Integrable Systems
2015-05-27 v2
Abstract
We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.
Keywords
Cite
@article{arxiv.1102.1239,
title = {Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs},
author = {Yoichi Nakata},
journal= {arXiv preprint arXiv:1102.1239},
year = {2015}
}
Comments
14 pages, 10 figures Added citations in v2