Soliton formulation by Moyal algebra

TL;DR

This paper introduces a novel formulation of lattice soliton equations using reduced Moyal algebra, bridging discrete and continuous soliton models through a parameter limit.

Contribution

It presents a new algebraic framework for lattice solitons that connects discrete and continuous equations via the Moyal algebra approach.

Findings

Formulation of lattice soliton equations using reduced Moyal algebra.

Demonstration that the continuous soliton equations emerge in a specific parameter limit.

Provides a unified algebraic perspective on soliton equations across discrete and continuous domains.

Abstract

We formulate the soliton equations on the lattice in terms of the reduced Moyal algebra which includes one parameter. The vanishing limit of the parameter leads to the continuous soliton equations.