Solutions to an autonomous discrete KdV equation via Painlev\'e-type ordinary difference equations
Exactly Solvable and Integrable Systems
2026-01-09 v4 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2503.06013,
title = {Solutions to an autonomous discrete KdV equation via Painlev\'e-type ordinary difference equations},
author = {Nobutaka Nakazono},
journal= {arXiv preprint arXiv:2503.06013},
year = {2026}
}
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14 pages