The Liouville integrable systems associated with a new discrete \(3\times 3\) matrix spectral problem

DOI10.1016/J.AMC.2009.08.061zbMath1179.39011OpenAlexW2055181391MaRDI QIDQ1044425

Xin-Yue Li, Qiu-Lan Zhao, Xi-Xiang Xu

Publication date: 18 December 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.08.061

zbMATH Keywords

conservation lawslattice systemsmatrix spectral problemdiscrete Hamiltonian structurediscrete trace identityLiouville integrable lattice equations

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Discrete version of topics in analysis (39A12)

Related Items (2)

The integrable coupling system of a \(3 \times 3\) discrete matrix spectral problem ⋮ Two families of Liouville integrable lattice equations

Cites Work

• Two hierarchies of integrable lattice equations associated with a discrete matrix spectral problem
• Nonlinearization of the Lax system for AKNS hierarchy
• Semi-direct sums of Lie algebras and continuous integrable couplings
• 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
• Positive and negative hierarchies of nonlinear integrable lattice models and three integrable coupling systems associated with a discrete spectral problem
• The Coupled Modified Korteweg-de Vries Equations
• Master Symmetries from Lax Operators for Certain Lattice Soliton Hierarchies
• Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions
• Integrable couplings of vector AKNS soliton equations
• Nonlinear differential−difference equations
• A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations
• A New Integrable Symplectic Map of Neumann Type
• Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations
• Bilinear Forms of Integrable Lattices Related to Toda and Lotka-Volterra Lattices
• A discrete variational identity on semi-direct sums of Lie algebras
• A trace identity and its applications to the theory of discrete integrable systems
• An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems

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