Integrable two-component systems of difference equations

DOI10.1098/rspa.2019.0668zbMath1439.39005arXiv1908.02413OpenAlexW3008868582MaRDI QIDQ5114248

Maciej Nieszporski, A. G. Tongas, V. G. Papageorgiou, Pavlos Kassotakis

Publication date: 21 June 2020

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.02413

zbMATH Keywords

Lax pairsintegrable difference equationsYang-Baxter maps.

Mathematics Subject Classification ID

Partial difference equations (39A14)

Related Items

Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps ⋮ On non-abelian quadrirational Yang–Baxter maps* ⋮ A revisit to the ABS H2 equation ⋮ Two-component Yang-Baxter maps and star-triangle relations ⋮ Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube ⋮ Multi-component extension of CAC systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symbolic computation of Lax pairs of partial difference equations using consistency around the cube
• Families of integrable equations
• Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere
• Lax pair for the Adler (lattice Krichever-Novikov) system
• Matrix Kadomtsev-Petviashvili equation: tropical limit, Yang-Baxter and pentagon maps
• Relativistic collisions as Yang-Baxter maps
• Yang-Baxter maps, discrete integrable equations and quantum groups
• Matrix KP: tropical limit and Yang-Baxter maps
• Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings
• Integrable noncommutative equations on quad-graphs. The consistency approach
• Classification of integrable equations on quad-graphs. The consistency approach
• On the \(3D\) consistency of a Grassmann extended lattice Boussinesq system
• Invariants in separated variables: Yang-Baxter, entwining and transfer maps
• On non-multiaffine consistent-around-the-cube lattice equations
• The discrete and continuous Painlevé VI hierarchy and the Garnier systems
• Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
• Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation
• Discrete Systems and Integrability
• Darboux transformations, finite reduction groups and related Yang–Baxter maps
• Multi-Quadratic Quad Equations: Integrable Cases from a Factorized-Discriminant Hypothesis
• Integrable lattice equations with vertex and bond variables
• Entwining Yang-Baxter maps and integrable lattices
• Difference systems in bond and face variables and non-potential versions of discrete integrable systems
• 3D compatible ternary systems and Yang–Baxter maps
• Grassmann extensions of Yang–Baxter maps
• Searching for CAC-maps
• Exact solutions of quantum mappings from the lattice KdV as multi-dimensional operator difference equations
• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• Geometric Crystals and Set-Theoretical Solutions to the Quantum Yang-Baxter Equation
• Set-theoretical reflection equation: classification of reflection maps
• Integrable maps which preserve functions with symmetries
• 2ⁿ-rational maps
• Discrete KP Equation and Momentum Mapping of Toda System
• On the lattice-geometry and birational group of the six-point multi-ratio equation
• Yang–Baxter maps and multi-field integrable lattice equations
• Entwining Yang–Baxter maps related to NLS type equations