Integrable discretisations of the noncommutative NLS equation
Abstract
Abstract We show how to derive noncommutative versions of integrable partial difference equations using Darboux transformations. As an illustrative example, we use the nonlinear Schrödinger system. We derive a noncommutative nonlinear Schrödinger equation and we construct its integrable discretisations via the compatibility condition of Darboux transformations around the square. In particular, we construct a noncommutative Adler–Yamilov type system and a noncommutative discrete Toda equation. For the noncommutative Adler–Yamilov type system we construct Bäcklund transformations.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Algebraic structures and combinatorial models
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Publisher
- IOP Publishing
- Volume
- 59
- Issue
- 4
- Pages
- 045203–045203
- Publication date
- 19 January 2026
- Language
- EN