Reductions in finite-dimensional integrable systems and special points of classical r-matrices

DOI10.1063/1.4972021zbMath1417.37207OpenAlexW2561536500MaRDI QIDQ2951766

T. V. Skrypnik

Publication date: 9 January 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4972021

zbMATH Keywords

\(r\)-matricesLax-integrable systems

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Exactly solvable models; Bethe ansatz (82B23) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Related Items (8)

On the general solution of the permuted classical Yang–Baxter equation and quasigraded Lie algebras ⋮ Anisotropic Z n-graded classical r-matrix, deformed A n Toda- and Gaudin-type models, and separation of variables ⋮ Reduction in soliton hierarchies and special points of classical \(r\)-matrices ⋮ Separation of variables in anisotropic models: anisotropic Rabi and elliptic Gaudin model in an external magnetic field ⋮ Separation of variables, quasi-trigonometric \(r\)-matrices and generalized Gaudin models ⋮ Separation of variables, Lax-integrable systems and \(gl(2) \otimes gl(2)\)-valued classical \(r\)-matrices ⋮ The generalized Lipkin-Meshkov-Glick model and the modified algebraic Bethe ansatz ⋮ On a class of gl(n) ⊗ gl(n)-valued classical r-matrices and separation of variables

Cites Work

• Unnamed Item
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• Decompositions of quasigraded Lie algebras, non-skew-symmetric classical \(r\)-matrices and generalized Gaudin models
• Quantum integrable models of interacting bosons and classical \(r\)-matrices with spectral parameters
• Bäcklund-Darboux transformation for classical Yang-Baxter bundles
• On the classical Young-Baxter equation for simple Lie algebras
• What is a classical r-matrix?
• Integrable quantum spin chains, non-skew symmetric \(r\)-matrices and quasigraded Lie algebras
• Lie algebras and Lax equations with spectral parameter on an elliptic curve
• The complex exponent of a singularity does not change along strata mu=const
• On rational solutions of Yang-Baxter equations. Maximal orders in loop algebra
• Dynamical systems VII. Integrable systems. Nonholonomic dynamical systems. Transl. from the Russian by A.G. Reyman and M.A. Semenov-Tian- Shansky
• Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
• Generalized shift elements and classical \(r\)-matrices: construction and applications
• New integrable Gaudin-type systems, classical \(r\)-matrices and quasigraded Lie algebras
• Special quasigraded Lie algebras and integrable Hamiltonian systems
• Bethe ansatz solutions of the Bose-Hubbard dimer
• The quantum Gaudin system
• “Many-poled” r-matrix Lie algebras, Lax operators, and integrable systems
• Integrable deformation of the Toda chain and quasigraded Lie algebras
• New non-skew symmetric classicalr-matrices and ‘twisted’ quasigraded Lie algebras
• Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz
• Integrability and superintegrability of the generalized n-level many-mode Jaynes–Cummings and Dicke models
• Alternate quantizations of the discrete self-trapping dimer
• General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters
• Infinite-dimensional Lie algebras, classical r-matrices, and Lax operators: Two approaches
• Generalized Gaudin systems in a magnetic field and non-skew-symmetricr-matrices
• Integrals of nonlinear equations of evolution and solitary waves
• Quadratic algebras and integrable systems

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