A discrete Darboux–Lax scheme for integrable difference equations

X. Fisenko, S. Konstantinou-Rizos and P. Xenitidis

Chaos, Solitons & Fractals, 2022, vol. 158, issue C

Abstract: We propose a discrete Darboux–Lax scheme for deriving auto-Bäcklund 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 Schrödinger (NLS) equation [7]. In particular, we construct an auto-Bäcklund 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.

Keywords: Darboux transformations; Bäcklund transformations; Quad-graph equations; Partial difference equations; Integrable lattice equations; 3D-consistency; Soliton solutions (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002697

DOI: 10.1016/j.chaos.2022.112059

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