On various integrable discretisations of a general two component Volterra system

TL;DR

This paper introduces two new integrable discretisations of a two-component Volterra system, deriving multisoliton solutions and a novel discrete Lotka-Volterra form through bilinearisation methods.

Contribution

The paper presents two distinct integrable discretisations of a bicomponent Volterra system and introduces a new discrete Lotka-Volterra equation via alternative bilinearisation.

Findings

Two integrable discretisations of the bicomponent Volterra system are constructed.

Multisoliton solutions are explicitly derived for the discretised systems.

A new discrete Lotka-Volterra equation is formulated through bilinearisation.

Abstract

We present two integrable discretisations of a general differential-difference bicomponent Volterra system. The results are obtained by discretising directly the corresponding Hirota bilinear equations in two different ways. Multisoliton solutions are presented together with a new discrete form of Lotka-Volterra equation obtained by an alternative bilinearisation.