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arXiv · 2503.06013

Solutions to an autonomous discrete KdV equation via Painlev\'e-type ordinary difference equations

Nobutaka Nakazono
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Abstract

Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show that a variation of Hirota's discrete KdV equation with an additional parameter admits two types of exact solutions: discrete Painlev\'e transcendent solutions and periodic solutions described by Painlev\'e-type ordinary difference equations.

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Nobutaka Nakazono. 2025-03-08. Solutions to an autonomous discrete KdV equation via Painlev\'e-type ordinary difference equations. https://arxiv.org/abs/2503.06013

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