A New Expression of Soliton Solution to the Ultradiscrete Toda Equation

TL;DR

This paper introduces a novel multi-soliton solution to the ultradiscrete Toda equation, providing a new expression and a direct proof, advancing the understanding of soliton solutions in ultradiscrete integrable systems.

Contribution

It presents a new form of multi-soliton solution and a direct proof for the ultradiscrete Toda equation, which was not previously available.

Findings

New multi-soliton solution proposed

Solution expressed in a perturbation form

Direct proof of the solution provided

Abstract

A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.