2000 character limit reached
A discrete Darboux-Lax scheme for integrable difference equations (2109.10372v1)
Published 21 Sep 2021 in nlin.SI, math-ph, and 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.