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

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

2011-12-12

arxiv.org/abs/1112.2419v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

4 pages

Scientific paper

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

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