A discrete Darboux-Lax scheme for integrable difference equations
Exactly Solvable and Integrable Systems
2022-04-27 v1 Mathematical Physics
math.MP
Abstract
We propose a discrete Darboux-Lax scheme for deriving auto-B\"acklund transformations and constructing solutions to quad-graph equations that do not necessarily possess the 3D consistency property. As an illustrative example we use the Adler-Yamilov type system which is related to the nonlinear Schr\"odinger (NLS) equation [19]. In particular, we construct an auto-B\"acklund transformation for this discrete system, its superposition principle, and we employ them in the construction of the one- and two-soliton solutions of the Adler-Yamilov system.
Cite
@article{arxiv.2109.10372,
title = {A discrete Darboux-Lax scheme for integrable difference equations},
author = {Xenia Fisenko and Sotiris Konstantinou-Rizos and Pavlos Xenitidis},
journal= {arXiv preprint arXiv:2109.10372},
year = {2022}
}
Comments
14 pages, 4 figures