Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations
Abstract
Hirota’s discrete Korteweg–de Vries (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.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Nonlinear Waves and Solitons
Differential Equations and Numerical Methods
Publication details
- Journal / source
- Journal of Mathematical Physics
- Volume
- 67
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN