Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

Shi, Y., Nimmo, J. J. C. and Zhang, D.-j. (2014) Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation. Journal of Physics A: Mathematical and Theoretical, 47(2), 025205. (doi: 10.1088/1751-8113/47/2/025205)

Abstract

The Hirota–Miwa equation can be written in 'nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Nimmo, Dr Jonathan
• Authors: Shi, Y., Nimmo, J. J. C., and Zhang, D.-j.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and Theoretical
• Publisher: IOP Publishing
• ISSN: 1751-8113
• ISSN (Online): 1751-8121