q-Painlevé VI equation arising from q-UC hierarchy
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چکیده
We study the q-difference analogue of the sixth Painlevé equation (q-PVI) by means of tau functions associated with affine Weyl group of type D5. We prove that a solution of q-PVI coincides with a self-similar solution of the q-UC hierarchy. As a consequence, we obtain in particular algebraic solutions of q-PVI in terms of the universal character which is a generalization of Schur polynomial attached to a pair of partitions.
منابع مشابه
On an integrable system of q-difference equations satisfied by the universal characters: its Lax formalism and an application to q-Painlevé equations
The universal character is a generalization of the Schur function attached to a pair of partitions. We study an integrable system of q-difference equations satisfied by the universal characters, which is an extension of the q-KP hierarchy and is called the lattice q-UC hierarchy. We describe the lattice q-UC hierarchy as a compatibility condition of its associated linear system (Lax formalism) ...
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تاریخ انتشار 2004