AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS

DOI10.1142/S0217979211101351zbMath1260.37035MaRDI QIDQ4911428

Lin Luo, Wen-Xiu Ma, En-gui Fan

Publication date: 15 March 2013

Published in: International Journal of Modern Physics B (Search for Journal in Brave)

zbMATH Keywords

zero-curvature representation{\(\tau\)}-symmetry algebracoupled integrable couplings

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (3)

Multi-component integrable couplings for the Ablowitz-Kaup-Newell-Segur and Volterra hierarchies ⋮ Bi-integrable couplings of a Kaup-Newell type soliton hierarchy and their bi-Hamiltonian structures ⋮ A family of integrable differential-difference equations: tri-Hamiltonian structure and Lie algebra of vector fields

Cites Work

• An approach for generating enlarging integrable systems
• Integrable theory of the perturbation equations.
• New symmetries for the Ablowitz-Ladik hierarchies
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Additional symmetries and string equation of the CKP hierarchy
• Bilinear Bäcklund transformations for the KP and \(k\)-constrained KP hierarchy
• A general approach for getting the commutator representations of the hierarchies of nonlinear evolution equations
• Algebraic structure of the operator related to stationary systems
• A simple method for generating integrable hierarchies with multi-potential functions
• ADDITIONAL SYMMETRIES OF KP, GRASSMANNIAN, AND THE STRING EQUATION
• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
• The multicomponent generalized Kaup–Newell hierarchy and its multicomponent integrable couplings system with two arbitrary functions
• K symmetries and tau symmetries of evolution equations and their Lie algebras
• COUPLING INTEGRABLE COUPLINGS
• THE ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH INTEGRABLE COUPLINGS
• An approach for constructing nonisospectral hierarchies of evolution equations
• The algebraic structures of isospectral Lax operators and applications to integrable equations
• Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
• The algebraic structure of zero curvature representations and application to coupled KdV systems
• Symmetries of the Kadomtsev-Petviashvili equation
• Abundant symmetries for the 1+1 dimensional classical Liouville field theory
• Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras

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