Solutions to the ultradiscrete KdV equation expressed as the maximum of a quadratic function

TL;DR

This paper introduces a class of solutions to the ultradiscrete KdV equation, expressed as the maximum of quadratic forms, encompassing soliton and pseudo-periodic solutions, using discrete convex analysis techniques.

Contribution

It presents a novel method to construct solutions to the ultradiscrete KdV equation via maximum of quadratic functions, expanding the solution space.

Findings

Includes soliton and pseudo-periodic solutions

Uses discrete convex analysis in proof

Provides a new solution construction method

Abstract

We propose the functions defined by the maximum of a discrete quadratic form and satisfying the ultradiscrete KdV equation. These functions includes not only soliton solutions but also pseudo-periodic solutions. In the proof, we employ some facts of discrete convex analysis.