A FAMILY OF DISCRETE INTEGRABLE COUPLING SYSTEMS AND ITS LIOUVILLE INTEGRABILITY

DOI10.1142/S0217984909019843zbMath1230.37088MaRDI QIDQ5192967

Xi-Xiang Xu, Hong-Xiang Yang

Publication date: 10 August 2009

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

zbMATH Keywords

Liouville integrabilitydiscrete integrable systemintegrable coupling systemdiscrete variational identitysemi-direct sum of Lie algebraHamiltonian form

Mathematics Subject Classification ID

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

Cites Work

• Positive and negative hierarchies of integrable lattice models associated with a Hamiltonian pair
• Integrable theory of the perturbation equations.
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Enlarging spectral problems to construct integrable couplings of soliton equations
• The conservation laws of some discrete soliton systems.
• Factorization of a hierarchy of the lattice soliton equations from a binary Bargmann symmetry constraint
• A hierarchy of discrete Hamiltonian equations and its binary nonlinearization by symmetry constraint
• Relativistic Toda systems
• Master Symmetries from Lax Operators for Certain Lattice Soliton Hierarchies
• Integrable couplings of vector AKNS soliton equations
• Nonlinear differential−difference equations
• A new hierarchy of integrable differential-difference equations and Darboux transformation
• R-matrix approach to lattice integrable systems
• A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations
• Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations
• A discrete variational identity on semi-direct sums of Lie algebras
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras

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