Two \(3 \times 3\) discrete matrix spectral problems and associated Liouville integrable lattice soliton equations

DOI10.1016/j.cnsns.2010.09.017zbMath1221.37151OpenAlexW2013797832MaRDI QIDQ718566

Yu-Qing Li

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.2010.09.017

zbMATH Keywords

Hamiltonian structureLiouville integrabilityLax pairdiscrete zero curvature representationlattice soliton equation

Mathematics Subject Classification ID

Difference operators (39A70) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lattice dynamics; integrable lattice equations (37K60)

Related Items (1)

Conservation laws and self-consistent sources for an integrable lattice hierarchy associated with a three-by-three discrete matrix spectral problem

Cites Work

• Positive and negative hierarchies of integrable lattice models associated with a Hamiltonian pair
• Two hierarchies of new nonlinear evolution equations associated with \(3 \times 3\) matrix spectral problems
• Two integrable differential-difference equations derived from the discrete BKP equation and their related equations
• The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy.
• New hierarchies of integrable positive and negative lattice models and Darboux transformation
• A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations
• Nonlinear differential−difference equations
• R-matrix approach to lattice integrable systems
• A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations
• A new integrable symplectic map associated with lattice soliton equations
• Integrable relativistic Toda type lattice hierarchies, associated coupling systems and the Darboux transformation
• A Hierarchy of Lax Integrable Lattice Equations, Liouville Integrability and a New Integrable Symplectic Map
• A trace identity and its applications to the theory of discrete integrable systems

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