Reductions of lattice mKdV to $q$-$\mathrm{P}_{VI}$
Christopher M. Ormerod
TL;DR
This paper introduces a reduction of the lattice mKdV equation leading to a $q$-analogue of the sixth Painlevé equation, providing the first ultradiscrete Lax representation of its ultradiscrete analogue.
Contribution
It presents a novel reduction method connecting lattice mKdV to $q$-$ ext{P}_{VI}$ and constructs the first ultradiscrete Lax representation for its ultradiscrete form.
Findings
Established a reduction from lattice mKdV to $q$-$ ext{P}_{VI}$
Developed the first ultradiscrete Lax representation for ultradiscrete $q$-$ ext{P}_{VI}$
Bridged continuous, discrete, and ultradiscrete integrable systems
Abstract
This Letter presents a reduction of the lattice modified Korteweg-de-Vries equation that gives rise to a -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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