Discretizations of the Landau-Lifshits equation

DOI10.1007/BF02551066zbMath0984.39010OpenAlexW2054267778MaRDI QIDQ5941969

Vsevolod Eduardovich Adler

Publication date: 14 May 2002

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02551066

zbMATH Keywords

Bäcklund transformationsintegrable systemHeisenberg spin chainLandau-Lifshits equationSklyanin chain

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Discrete version of topics in analysis (39A12)

Related Items (10)

Lax pair for the Adler (lattice Krichever-Novikov) system ⋮ Small \(C^1\)-smooth perturbations of skew products and the partial integrability property ⋮ Darboux transformations and recursion operators for differential-difference equations ⋮ Geometrically integrable maps in the plane and their periodic orbits ⋮ Integrable Discretizations of Some Cases of the Rigid Body Dynamics ⋮ Quasiperiodic Solutions of the Heisenberg Ferromagnet Hierarchy ⋮ Discrete time Toda systems ⋮ Symmetries of Spectral Problems ⋮ Action as an invariant of Bäcklund transformations for Lagrangian systems ⋮ Integrability of Adler's discretization of the Neumann system

Cites Work

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• Some algebraic structures connected with the Yang-Baxter equation
• Generalized Schrödinger equations and Jordan pairs
• Generalized Legendre transformations
• Integrable lattices
• Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
• Multi-component Volterra and Toda type integrable equations
• The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems
• Integrable maps
• A unified algebraic approach to integral and discrete evolution equations
• Multicomponent generalization of the hierarchy of the Landau-Lifshits equation

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