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arXiv · 2507.11670

Integrable discretisations of the noncommutative NLS equation

S. Konstantinou-Rizos·P. Xenitidis
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Abstract

We show how to derive noncommutative versions of integrable partial difference equations using Darboux transformations. As an illustrative example, we use the nonlinear Schr\"odinger (NLS) system. We derive a noncommutative nonlinear Schr\"odinger 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 B\"acklund transformations.

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BibTeXRIS

S. Konstantinou-Rizos, P. Xenitidis. 2025-07-15. Integrable discretisations of the noncommutative NLS equation. https://arxiv.org/abs/2507.11670

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