Integrable extensions of the Adler map via Grassmann algebras

DOI10.1134/S0040577921050019zbMath1467.37058arXiv2012.15121OpenAlexW3175190728MaRDI QIDQ2036370

S. Konstantinou-Rizos, Panagiota Adamopoulou, Georgios Papamikos

Publication date: 29 June 2021

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.15121

zbMATH Keywords

Liouville integrabilitysymplectic structurediscrete dynamical systemGrassmann algebraYang-Baxter map

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Exterior algebra, Grassmann algebras (15A75) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37) Integrable difference and lattice equations; integrability tests (39A36) Completely integrable discrete dynamical systems (37J70) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items

Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps ⋮ Discrete integrable systems associated with relativistic collisions

Cites Work

• Unnamed Item
• Unnamed Item
• Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras
• Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere
• Completely integrable symplectic mapping
• Classical limits of the SU(2)-invariant solutions of the Yang-Baxter equation
• Recuttings of polygons
• Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings
• On the \(3D\) consistency of a Grassmann extended lattice Boussinesq system
• Bäcklund-Darboux transformations and discretizations of super KdV equation
• Darboux transformations, finite reduction groups and related Yang–Baxter maps
• Supersymmetric KdV equation: Darboux transformation and discrete systems
• Periodic cluster mutations and related integrable maps
• Entwining Yang-Baxter maps and integrable lattices
• Grassmann extensions of Yang–Baxter maps
• Anticommutative extension of the Adler map
• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• A Supersymmetric AKNS Problem and Its Darboux‐Bäcklund Transformations and Discrete Systems
• Yang–Baxter maps with first-degree-polynomial 2 × 2 Lax matrices
• Integrable maps
• The Yang-Baxter transformation
• A noncommutative discrete potential KdV lift
• Set-theoretical reflection equation: classification of reflection maps
• Yang–Baxter and reflection maps from vector solitons with a boundary
• Lax Matrices for Yang-Baxter Maps
• Entwining Yang–Baxter maps related to NLS type equations