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

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 Painlevé transcendent solutions and periodic solutions described by Painlevé-type ordinary difference equations.

preprint2026arXivOpen access
Nobutaka Nakazono
math-phmath.MPnlin.SI
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Nobutaka Nakazono

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