Corpus ID: 237593037

A discrete Darboux-Lax scheme for integrable difference equations

@inproceedings{Fisenko2021ADD,
  title={A discrete Darboux-Lax scheme for integrable difference equations},
  author={Xenia Fisenko and S. Konstantinou-Rizos and Pavlos Xenitidis},
  year={2021}
}
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 [19]. In particular, we construct an auto-Bäcklund transformation for this discrete system, its superposition principle, and we employ them in the construction of the oneand two… Expand

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