Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

Details Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

2011-02-07

arxiv.org/abs/1102.1239v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, 10 figures Added citations in v2

Scientific paper

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.

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