Non-commutative q-Painleve VI equation

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.

7 pages, 1 figure; introduction expanded (version 2)

References in corpus (4)

• Non-commutative rational Yang-Baxter maps
• Non-commutative lattice modified Gel'fand-Dikii systems
• A q-analogue of gl_3 hierarchy and q-Painleve VI
• Desargues maps and their reductions

Cited by in corpus (3)

• The Coxeter relations and KP map for non-commuting symbols
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Discrete Lax pairs and hierarchies of integrable difference systems