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|Title:||On elliptic Lax systems on the lattice and a compound theorem for hyperdeterminants|
|Citation:||Delice, N., Nijhoff, F. W., & Yoo-Kong, S. (2014). On elliptic Lax systems on the lattice and a compound theorem for hyperdeterminants. Journal of Physics A: Mathematical and Theoretical, 48(3), 035206. https://doi.org/10.1088/1751-8113/48/3/035206|
|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 Adler’s lattice). We present the general scheme, but focus mainly of 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 analysed using Cayley’s hyperdeterminant of format 2×2×2, yielding a multi-component system of coupled 3-leg quad-equations.|
|Appears in Collections:||Research|
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