Fisenko, Xenia and Konstantinou-Rizos, Sotiris and Xenitidis, Pavlos (2022) A discrete Darboux-Lax scheme for integrable difference equations. Chaos, Solitons & Fractals: An interdisciplinary journal of nonlinear science, 158. ISSN 0960-0779 (Accepted for Publication)
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Abstract
We propose a discrete Darboux-Lax scheme for deriving auto-Backlund 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 Schroedinger (NLS) equation [21]. In particular, we construct an auto-Backlund 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.
| Item Type: | Article |
|---|---|
| Additional Information and Comments: | NOTICE: this is the author’s version of a work that was accepted for publication in Chaos, Solitons and Fractals. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available from: https://www.sciencedirect.com/science/article/pii/S0960077922002697 |
| Keywords: | Darboux transformations, Backlund transformations, quad-graph equations, partial difference equations, integrable lattice equations, 3D-consistency, soliton solutions. |
| Faculty / Department: | Faculty of Human and Digital Sciences > School of Computer Science and the Environment |
| Depositing User: | Pavlos Xenitidis |
| Date Deposited: | 04 Apr 2022 13:52 |
| Last Modified: | 14 Jan 2025 16:33 |
| URI: | https://hira.hope.ac.uk/id/eprint/3512 |
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