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

preprint2011arXivOpen access

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.

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

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Reductions of lattice mKdV to qqq-PVI\mathrm{P}_{VI}PVI​

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