A q-analogue of gl_3 hierarchy and q-Painleve VI

Abstract

A q-analogue of the gl_3 Drinfel'd-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painleve VI equation proposed by Jimbo and Sakai.

arXiv comment14 pages, IOP style, to appear in J. Phys. A Special issue "One hundred years of Painleve VI"

References in corpus (7)

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• The solution to the q-KdV equation
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Cited by in corpus (5)

• Reductions of lattice mKdV to $q$-${\mathrm{P}}_{VI}$
• On an integrable system of q-difference equations satisfied by the universal characters: its Lax formalism and an application to q-Painleve equations
• Discretisations of constrained KP hierarchies
• A q-analogue of the Drinfeld-Sokolov hierarchy of type A and q-Painleve system
• Non-commutative q-Painleve VI equation