Reductions of lattice mKdV to $q$-${\mathrm{P}}_{VI}$

Abstract

This Letter presents a reduction of the lattice modified Korteweg-de-Vries equation that gives rise to a $q$-analogue of the sixth Painlevé equation. This new approach allows us to give the first ultradiscrete Lax representation of an ultradiscrete analogue of the sixth Painlevé equation.

4 pages

References in corpus (1)

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

Cited by in corpus (17)

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• The discrete mKdV equation revisited: a Riemann-Hilbert approach