Central extension approach to integrable field and lattice-field systems in \((2+1)\)-dimensions

DOI10.1016/S0034-4877(99)80143-8zbMath0970.37060MaRDI QIDQ1573855

Andrzej Szum, Maciej Błaszak, Anatoliy K. Prykarpatsky

Publication date: 9 August 2000

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

\(R\)-matrixlattice systems\((2+1)\)-dimensional integrable Hamiltonian

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lattice dynamics; integrable lattice equations (37K60)

Related Items (8)

The Bargmann type reduction for some Lax integrable two-dimensional generalization of the relativistic Toda lattice ⋮ A Few Integrable Dynamical Systems, Recurrence Operators, Expanding Integrable Models and Hamiltonian Structures by the r -Matrix Method ⋮ Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations ⋮ Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations ⋮ A discrete nonlinear Schrödinger-type hierarchy, its finite-dimensional reduction analysis, and the numerical integration scheme ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators ⋮ Gauge Transformation and Reciprocal Link for (2+1)-Dimensional Integrable Field Systems ⋮ Discrete approximations on functional classes for the integrable nonlinear Schrödinger dynamical system: a symplectic finite-dimensional reduction approach

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• Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. II. The reduction via Dirac and canonical quantization procedure
• R-matrix approach to lattice integrable systems
• Dressing transformations and Poisson group actions

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