Non-commutative q-Painleve VI equation

2013/10/31 by Adam Doliwa · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.DS #math.MP

paper · pdf · doi:10.1088/1751-8113/47/3/035203

published as J. Phys. A: Math. Theor. 47 (2014) 035203 · 7 pages, 1 figure; introduction expanded (version 2)

arxiv created 2013/11/22 · arxiv updated 2014/02/19

Abstract

By applying suitable centrality condition to non-commutative non-isospectral lattice modified Gel'fand-Dikii type systems we obtain the corresponding non-autonomous equations. Then we derive non-commutative q-discrete Painleve VI equation with full range of parameters as the (2,2) similarity reduction of the non-commutative, non-isospectral and non-autonomous lattice modified Korteweg-de Vries equation. We also comment on the fact that in making the analogous reduction starting from Schwarzian Korteweg-de Vries equation no such "non-isospectral generalization" is needed.

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