Vertex operator for the non-autonomous ultradiscrete KP equation

TL;DR

This paper introduces an ultradiscrete vertex operator for the ultradiscrete KP equation, enabling the generation of N+1-soliton solutions from N-soliton solutions, thus advancing the understanding of ultradiscrete integrable systems.

Contribution

It presents a novel ultradiscrete vertex operator applicable to the ultradiscrete KP equation and related equations, expanding solution construction methods.

Findings

Constructed an ultradiscrete vertex operator for the ultradiscrete KP equation.

Demonstrated the operator's ability to generate higher soliton solutions.

Extended the approach to other ultradiscrete equations.

Abstract

We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.