A multidimensionally consistent version of Hirota's discrete KdV equation

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.

11 pages, 2 figures

References in corpus (2)

• On non-multiaffine consistent-around-the-cube lattice equations
• Bilinearization and Casorati determinant solution to the non-autonomous discrete KdV equation

Cited by in corpus (12)

• Symbolic Computation of Lax Pairs of Partial Difference Equations Using Consistency Around the Cube
• Direct linearising transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations
• On non-multiaffine consistent-around-the-cube lattice equations
• Difference systems in bond and face variables and non-potential versions of discrete integrable systems
• Idempotent biquadratics, Yang-Baxter maps and birational representations of Coxeter groups
• On reductions of the discrete Kadomtsev--Petviashvili-type equations
• Desargues maps and their reductions
• Discrete Darboux system with self-consistent sources and its symmetric reduction
• Systems of difference equations on a vector valued function that admit 3D space of scalar potentials
• Multi-quadratic quad equations: integrable cases from a factorised-discriminant hypothesis
• On the three-dimensional consistency of Hirota's discrete Korteweg-de Vries Equation
• $2^n-$rational maps