Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation
Exactly Solvable and Integrable Systems
2017-05-30 v1 Mathematical Physics
math.MP
Abstract
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.
Cite
@article{arxiv.1705.09896,
title = {Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation},
author = {Ying Shi and Jonathan Nimmo and Junxiao Zhao},
journal= {arXiv preprint arXiv:1705.09896},
year = {2017}
}