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arXiv · 1310.6890

Non-commutative q-Painleve VI equation

Adam Doliwa
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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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Adam Doliwa. 2013-11-22. Non-commutative q-Painleve VI equation. https://doi.org/10.1088/1751-8113%2F47%2F3%2F035203

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