A hierarchy of nonlinear differential-difference equations and a new Bargmann type integrable system

DOI10.1016/j.physleta.2006.05.084zbMath1236.37039OpenAlexW1994484665MaRDI QIDQ942547

Xi-Xiang Xu, Ye-Peng Sun, Deng-Yuan Chen

Publication date: 5 September 2008

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2006.05.084

zbMATH Keywords

Hamiltonian structureLiouville integrabilitydifferential-difference equationbinary nonlinearization

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (10)

New hierarchies of integrable lattice equations and associated properties: Darboux transformation, conservation laws and integrable coupling ⋮ Positive and negative integrable lattice hierarchies: conservation laws and \(N\)-fold Darboux transformations ⋮ TWO HIERARCHIES OF NONLINEAR SOLITON EQUATIONS, NEW INTEGRABLE SYMPLECTIC MAP AND DISCRETE INTEGRABLE COUPLINGS ⋮ A hierarchy of non-isospectral multi-component AKNS equations and its integrable couplings ⋮ A hierarchy of Liouville integrable lattice equations and its integrable coupling systems ⋮ SOME EXPANDING SEMI-DIRECT SUMS OF LIE ALGEBRA $\bar{G}$ AND ITS APPLICATION ⋮ New non-isospectral integrable couplings of the AKNS system ⋮ A family of integrable differential-difference equations: tri-Hamiltonian structure and Lie algebra of vector fields ⋮ Characters of explicit solutions for a semidiscrete integrable coupled equation ⋮ New Integrable Multicomponent Nonlinear Partial Differential-Difference Equations

Cites Work

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• A new hierarchy of integrable differential-difference equations and Darboux transformation
• New Liouville integrable noncanonical Hamiltonian systems from the AKNS spectral problem
• Restricted flows of the Ablowitz-Ladik hierarchy and their continuous limits
• From the special 2 + 1 Toda lattice to the Kadomtsev-Petviashvili equation
• An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems

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