Vertex operator for the ultradiscrete KdV equation

TL;DR

This paper introduces an ultradiscrete vertex operator for the ultradiscrete KdV equation, enabling the generation of higher-soliton solutions from existing ones, thus advancing the understanding of soliton dynamics in ultradiscrete systems.

Contribution

It presents the first ultradiscrete vertex operator that systematically constructs N+1-soliton solutions from N-soliton solutions.

Findings

Successfully defines the ultradiscrete vertex operator.

Demonstrates the operator's ability to generate higher-order soliton solutions.

Provides a new tool for analyzing ultradiscrete integrable systems.

Abstract

We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KdV equation, which maps N-soliton solutions to N+1-soliton ones.