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arXiv · 2109.10372

A discrete Darboux-Lax scheme for integrable difference equations

Xenia Fisenko·Sotiris Konstantinou-Rizos·Pavlos Xenitidis
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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.

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Xenia Fisenko, Sotiris Konstantinou-Rizos, Pavlos Xenitidis. 2021-09-21. A discrete Darboux-Lax scheme for integrable difference equations. https://doi.org/10.1016/j.chaos.2022.112059

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