Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs
arXiv:1102.1239 · doi:10.1088/1751-8113/44/29/295204
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 Bäcklund 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.
14 pages, 10 figures Added citations in v2