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arXiv · 1703.09215

Reduction of lattice equations to the Painlevé equations: P$_{\rm IV}$ and P$_{\rm V}$

Nobutaka Nakazono
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Abstract

In this paper, we construct a new relation between ABS equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

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Nobutaka Nakazono. 2018-01-06. Reduction of lattice equations to the Painlevé equations: P$_{\rm IV}$ and P$_{\rm V}$. https://doi.org/10.1063/1.5023252

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