On some class of partial difference equations admitting a zero-curvature representation

2014/09/24 by Andrei K. Svinin, Svinin, Andrei K.
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1409.6784

11 pages. arXiv admin note: substantial text overlap with arXiv:1304.7310

arxiv created 2014/09/24 · arxiv updated 2014/09/25

Abstract

We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized symmetries for obtained class of partial difference equations. As a byproduct we also derive non-evolutionary differential-difference equations with their Lax pair representation which may be of potential interest.

Citations

• On some class of differential-difference equations admitting Lax representation

Related

• On some class of differential-difference equations admitting Lax representation
• Lectures on nonlinear integrable equations and their solutions
• Classification of evolutionary equations on the lattice. I. The general theory
• On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation
• Bilinear Differential-Difference Equations and One-Point Distributions of Some KPZ-Class Models