Discrete and Ultradiscrete Mixed Soliton Solutions

TL;DR

This paper introduces a new soliton equation derived from the generalized discrete BKP equation, featuring two types of solutions with opposite properties, and extends these to ultradiscrete analogues that relate to the Box-Ball system.

Contribution

It presents a novel soliton equation with dual solution types and develops their ultradiscrete analogues, connecting to the Box-Ball system.

Findings

The new soliton equation admits two solution types with opposite amplitude and velocity signs.

Ultradiscrete analogues preserve the properties of the original solutions.

The ultradiscrete system relates to the well-known Box-Ball system.

Abstract

We propose a new type of soliton equation, which is obtained from the generalized discrete BKP equation. The obtained equation admits two types of soliton solutions. The signs of amplitude and velocity of the soliton solution are opposite to the other. We also propose the ultradiscrete analogues of them. The ultradiscrete equation also admits the similar properties. In particular it behaves the original Box-Ball system in a special case.