Delice, N, Nijhoff, FW and Yoo-Kong, S (2015) On elliptic Lax systems on the lattice and a compound theorem for hyperdeterminants. Journal of Physics A: Mathematical and Theoretical, 48 (3). ISSN 1751-8113
Abstract
A general elliptic N × N matrix Lax scheme is presented, leading to two classes of elliptic lattice systems, one which we interpret as the higher-rank analogue of the Landau-Lifschitz equations, while the other class we characterize as the higher-rank analogue of the lattice Krichever-Novikov equation (or Adlers lattice). We present the general scheme, but focus mainly on the latter type of models. In the case N = 2 we obtain a novel Lax representation of Adlers elliptic lattice equation in its so-called 3-leg form. The case of rank N = 3 is analyzed using Cayleys hyperdeterminant of format , yielding a multi-component system of coupled 3-leg quad-equations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Compound theorem; elliptic lattice systems; elliptic Lax systems; hyperdeterminants |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Feb 2015 10:43 |
Last Modified: | 03 May 2015 07:41 |
Published Version: | http://dx.doi.org/10.1088/1751-8113/48/3/035206 |
Status: | Published |
Publisher: | Institute of Physics Publishing |
Identification Number: | 10.1088/1751-8113/48/3/035206 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:82862 |