A lattice hierarchy and its continuous limits

DOI10.1016/j.physleta.2008.08.052zbMath1225.82010OpenAlexW1985486039MaRDI QIDQ644065

En-gui Fan

Publication date: 2 November 2011

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

Full work available at URL: https://doi.org/10.1016/j.physleta.2008.08.052

zbMATH Keywords

Hamiltonian structureAKNS hierarchycontinuous limitlattice hierarchy

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Continuum limits in quantum field theory (81T27) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10)

Related Items

A KIND OF NEW CONTINUOUS LIMITS OF AN INTEGRABLE COUPLING SYSTEM FOR DISCRETE AKNS HIERARCHY ⋮ Continuous limits for an integrable coupling of the Kac-Van Moerbeke hierarchy ⋮ An integrable coupling system of lattice hierarchy and its continuous limits ⋮ Continuous limits for an integrable coupling system of Toda equation hierarchy ⋮ New form \((2+1)\)-dimensional integrable lattice hierarchies with two shift operators Ẽ and Ê ⋮ An integrable coupling family of Merola-Ragnisco-Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family

Cites Work

• The Toda hierarchy and the KdV hierarchy
• Semi-direct sums of Lie algebras and continuous integrable couplings
• A lattice hierarchy with a free function and its reductions to the Ablowitz-Ladik and Volterra hierarchies
• Theory of nonlinear lattices.
• On the continuous limit of integrable lattices. I: The Kac-Moerbeke system and KdV theory
• On the geometry of Darboux transformations for the KP hierarchy and its connection with the discrete KP hierarchy
• The relation between the Toda hierarchy and the KdV hierarchy
• Analytical Bethe ansatz, canonical Bäcklund transformation and \(Q\)-operator for a new discrete integrable hierarchy
• Master Symmetries from Lax Operators for Certain Lattice Soliton Hierarchies
• Symmetries as integrability criteria for differential difference equations
• A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions
• Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure
• Nonlinear differential−difference equations
• On some integrable systems related to the Toda lattice
• A novel hierarchy of integrable lattices
• Nonisospectral negative Volterra flows and mixed Volterra flows: Lax pairs, infinitely many conservation laws and integrable time discretization
• A discrete Schr dinger spectral problem and associated evolution equations
• Explicit auto-transformations of integrable chains
• Restricted flows of the Ablowitz-Ladik hierarchy and their continuous limits

This page was built for publication: A lattice hierarchy and its continuous limits