2019/08/31 by S. Konstantinou-Rizos, Sotiris Konstantinou-Rizos · 16 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Consistency (knowledge bases) #Geometry #Lattice (music) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Theoretical physics #math-ph #math.MP #nlin.SI
paper · pdf · open access · doi:10.1016/j.nuclphysb.2019.114878
published in Nuclear Physics B 951, 114878 (Elsevier BV) · 23 pages, 5 figures
openalex publication_date 2019/11/29 · arxiv created 2020/05/29 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we formulate a "Grassmann extension" scheme for constructing noncommutative (Grassmann) extensions of Yang-Baxter maps together with their associated systems of PΔEs, based on the ideas presented in \citeSokor-Kouloukas. Using this scheme, we first construct a Grassmann extension of a Yang-Baxter map which constitutes a lift of a lattice Boussinesq system. The Grassmann-extended Yang-Baxter map can be squeezed down to a novel, integrable, Grassmann lattice Boussinesq system, and we derive its 3D-consistent limit. We show that some systems retain their 3D-consistency property in their Grassmann extension.