Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems

DOI10.1016/j.physleta.2008.10.020zbMath1227.37013arXiv0807.1294OpenAlexW2079998099MaRDI QIDQ646944

Artur Sergyeyev, Błażej M. Szablikowski

Publication date: 30 November 2011

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.1294

zbMATH Keywords

integrable systems\(R\)-matrixcentral extension(2+1)-dimensional bi-Hamiltonian systemscotangent universal hierarchy

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Central extensions and Schur multipliers (19C09)

Related Items (16)

An Algebraic Background for Hierarchies of PDE in Dimension (2|1) ⋮ Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. II ⋮ Complete classification of local conservation laws for generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I ⋮ New integrable differential-difference and fractional nonlinear dynamical systems and their algebro-analytical properties ⋮ The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure ⋮ Bi-Hamiltonian nature of the equation utx = uxyuy – uyyux ⋮ A note on the hyper-CR equation, and gauged \(N=2\) supergravity ⋮ Nonexistence of local conservation laws for generalized Swift-Hohenberg equation ⋮ Bi-Hamiltonian systems in \((2+1)\) and higher dimensions defined by Novikov algebras ⋮ Classical M. A. Buhl problem, its Pfeiffer-Sato solutions, and the classical Lagrange-d'Alembert principle for the integrable heavenly-type nonlinear equations ⋮ Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators ⋮ Recursion operators for multidimensional integrable PDEs ⋮ Hierarchies of Manakov-Santini type by means of Rota-Baxter and other identities

Cites Work

• Unnamed Item
• Recursion operators and bi-Hamiltonian structures in multidimensions. II
• Hamiltonian structure of Kadomtsev-Petviashvili type equations
• On the theory of recursion operator
• Recursion operators and bi-Hamiltonian structures in multidimensions. I
• On the integrability of \((2+1)\)-dimensional quasilinear systems
• Looped cotangent Virasoro algebra and nonlinear integrable systems in dimension \(2+1\)
• Hydrodynamic reductions and solutions of a universal hierarchy
• Universal models of soliton hierarchies
• Dark Equations
• Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations
• An interpolating dispersionless integrable system
• Multidimensional integrable systems and deformations of Lie algebra homomorphisms
• Towards classification of -dimensional integrable equations. Integrability conditions I
• Hamiltonian theory over noncommutative rings and integrability in multidimensions
• ClassicalR-matrix theory of dispersionless systems: II. (2   1) dimension theory
• Towards a Theory of Differential Constraints of a Hydrodynamic Hierarchy
• Integrable hydrodynamic chains
• Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability
• The spectral theory of a functional-difference operator in conformal field theory
• Universal Solitonic Hierarchy
• Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type

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