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. PACS numbers02.30.Ik, 02.90.+p, 03.65.Fd Mathematics subject classification 202037K60, 39A36, 35Q55, 16T25.
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