Special solutions to five autonomous integrable partial difference equations via the third and sixth Painlevé equations and the Garnier system in two variables

2026/03/01 by Nobutaka Nakazono · 1 voice
Physics and Astronomy · #math-ph #nlin.SI

paper · pdf · doi:10.1088/1751-8121/ae767e

arxiv published 2026/03/01 · arxiv updated 2026/05/01

Abstract

In this paper, we study special solutions of five autonomous integrable partial difference equations (PΔEs). More precisely, we show that these PΔEs admit special solutions that are described by non-autonomous ordinary difference equations arising from Bäcklund transformations of the third and sixth Painlevé equations and the Garnier system in two variables. This result provides a new perspective on the relationship between autonomous integrable PΔEs and Painlevé-type dynamics.

Citations

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Discussions

• Nobutaka Nakazono: Solutions to autonomous partial difference equations via the third and sixth Painlev\'e equations and the Garnier system in two variables https://arxiv.org/abs/2603.01087 https://ar [bsky, 0 points, 0 comments]

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• Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations