Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 48, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/48/3/035206
Keywords
hyperdeterminants; elliptic Lax systems; compound theorem; elliptic lattice systems
Categories
Funding
- Turkish Ministry of National Education
- EPSRC [EP/I002294/1, EP/I038683/1]
- Thailand Research Fund (TRF) [TRG5680081]
- EPSRC [EP/I002294/1, EP/I038683/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I002294/1, EP/I038683/1] Funding Source: researchfish
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A general elliptic N x 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 Adler's 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 Adler's elliptic lattice equation in its so-called 3-leg form. The case of rank N = 3 is analyzed using Cayley's hyperdeterminant of format 2x2x2, yielding a multi-component system of coupled 3-leg quad-equations.
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