A discrete Darboux-Lax scheme for integrable difference equations
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 numbers. 02.30.Ik, 02.90.+p, 03.65.Fd Mathematics subject classification 2020. 37K60, 39A36, 35Q55, 16T25.- Publication:
-
Chaos Solitons and Fractals
- Pub Date:
- May 2022
- DOI:
- 10.1016/j.chaos.2022.112059
- arXiv:
- arXiv:2109.10372
- Bibcode:
- 2022CSF...15812059F
- Keywords:
-
- Darboux transformations;
- Bäcklund transformations;
- Quad-graph equations;
- Partial difference equations;
- Integrable lattice equations;
- 3D-consistency;
- Soliton solutions;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- 37K60;
- 39A36;
- 35Q55;
- 16T25
- E-Print:
- 14 pages, 4 figures