Noncommutative Boussinesq and NLS type 2- and 3-simplex maps

2025/01/21 by Konstantinou-Rizos, S., Kutuzova, A. A. · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2501.12462

Abstract

We construct noncommutative maps related to the Boussinesq and Nonlinear Schrödinger (NLS) equations with their variables belonging to a noncommutative division ring. We show that the noncommutative Boussinesq type map satisfies the Yang--Baxter equation, and it can be squeezed down to a noncommutative version of the Boussinesq lattice equation. Moreover, we show that the noncommutative NLS type map is a Zamolodchikov tetrahedron map.

Cited by

• Noncommutative NLS systems: Darboux--Bäcklund transformations and integrable discretisations

Related

• Yang--Baxter maps of KdV, NLS and DNLS type on division rings
• Noncommutative NLS systems: Darboux--Bäcklund transformations and integrable discretisations
• Integrable discretisations of the noncommutative NLS equation
• Non-commutative rational Yang-Baxter maps
• Nonlinear Schrödinger type tetrahedron maps