arXiv 1703.034982017-03math-phmath.MPnlin.SI

Elliptic Painlevé equations from next-nearest-neighbor translations on the $E_8^{(1)}$ lattice

Nalini Joshi, Nobutaka Nakazono

备注：: 14 pages, 1 figure
DOI：: 10.1088/1751-8121/aa7915

英文摘要：

The well known elliptic discrete Painlevé equation of Sakai is constructed by a standard translation on the $E_8^{(1)}$ lattice, given by nearest neighbor vectors. In this paper, we give a new elliptic discrete Painlevé equation obtained by translations along next-nearest-neighbor vectors. This equation is a generic (8-parameter) version of a 2-parameter elliptic difference equation found by reduction from Adler's partial difference equation, the so-called Q4 equation. We also provide a projective reduction of the well known equation of Sakai.

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