Solutions to the ultradiscrete KP hierarchy and its reductions

TL;DR

This paper introduces a recursive method for solving the ultradiscrete KP hierarchy, a key equation in discrete soliton theory, and explores its solutions and compatibility conditions.

Contribution

It presents a novel recursive representation for solutions to the ultradiscrete KP hierarchy and introduces a class of initial solutions for the recursion.

Findings

Recursive solution representation for ultradiscrete KP hierarchy

A new class of initial solutions for the recursion

Analysis of compatibility conditions of ultradiscrete soliton equations

Abstract

We propose a recursive representation of solutions to an ultradiscrete analogue of the discrete KP hierarchy, which is the master equation of discrete soliton equations. We also propose a class of solutions which can be used to start the recursion. Finally, as an application, we discuss the compatibility condition of ultradiscrete soliton equations.