A multidimensionally consistent version of Hirota's discrete KdV equation

TL;DR

This paper introduces a new multidimensionally consistent version of Hirota's discrete KdV equation, expanding the class of integrable discrete models with quadratic polynomial structure and soliton solutions.

Contribution

It proposes a novel multidimensional generalisation of Hirota's discrete KdV equation based on a quadratic polynomial, including soliton solutions and insights into its algebraic properties.

Findings

The model is multidimensionally consistent.

Soliton solutions are explicitly constructed.

Discriminant factorisation links to other integrable models.

Abstract

A multidimensionally consistent generalisation of Hirota's discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as superposition principle are given. It is discussed how an important property of the defining polynomial, a factorisation of discriminants, appears also in the few other known discrete integrable multi-quadratic models.