Non-commutativeq-Painlevé VI equation

DOI10.1088/1751-8113/47/3/035203zbMATH Open1306.37072arXiv1310.6890OpenAlexW2075858877WikidataQ104434186 ScholiaQ104434186MaRDI QIDQ5402223

Adam Doliwa

Publication date: 6 March 2014

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1310.6890

zbMATH Keywords

discrete Painlevé equationsnon-commutative integrable systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Other functions coming from differential, difference and integral equations (33E30) Difference equations, scaling ((q)-differences) (39A13)

Related Items (5)

Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps ⋮ Non-integrability of some Painlevé VI-equations and dilogarithms ⋮ The Coxeter relations and KP map for non-commuting symbols ⋮ CFT approach to the q-Painlevé VI equation ⋮ Noncommutative Toda chains, Hankel quasideterminants and the Painlevé II equation

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