A three-parameter difference Hamiltonian operator, corresponding pair of Hamiltonian operators and a family of Liouville integrable lattice equations

DOI10.1016/j.cnsns.2009.05.057zbMath1221.37154OpenAlexW2011081796MaRDI QIDQ718213

Xi-Xiang Xu

Publication date: 23 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2009.05.057

zbMATH Keywords

Liouville integrableintegrable lattice equationdiscrete zero curvature representationbi-Hamiltonian formulationdifference Hamiltonian operator

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Difference operators (39A70) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lattice dynamics; integrable lattice equations (37K60)

Cites Work

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• Darboux transformation of a coupled lattice soliton equation
• Positive and negative hierarchies of integrable lattice models associated with a Hamiltonian pair
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Theory of nonlinear lattices
• Relativistic Toda systems
• Nonlinear differential−difference equations
• A simple model of the integrable Hamiltonian equation
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• A coupled AKNS–Kaup–Newell soliton hierarchy
• 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

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