Entwining Yang–Baxter maps over Grassmann algebras

IF 2.7 3区 数学 Q1 MATHEMATICS, APPLIED Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI:10.1016/j.physd.2024.134469
P. Adamopoulou , G. Papamikos
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引用次数: 0

Abstract

In this work we construct novel solutions to the set-theoretical entwining Yang–Baxter equation. These solutions are birational maps involving non-commutative dynamical variables which are elements of the Grassmann algebra of order n. The maps arise from refactorisation problems of Lax supermatrices associated to a nonlinear Schrödinger equation. In this non-commutative setting, we construct a spectral curve associated to each of the obtained maps using the characteristic function of its monodromy supermatrix. We find generating functions of invariants for the entwining Yang–Baxter maps from the moduli of the spectral curves. Moreover, we show that a hierarchy of birational entwining Yang–Baxter maps with commutative variables can be obtained by fixing the order n of the Grassmann algebra, and we present the cases n=1 (dual numbers) and n=2. Then we discuss the integrability properties, such as Lax matrices, invariants, and measure preservation, for the obtained discrete dynamical systems.
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来源期刊
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena 物理-物理:数学物理
CiteScore
7.30
自引率
7.50%
发文量
213
审稿时长
65 days
期刊介绍: Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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