On the hierarchy of the Landau-Lifshitz equation

DOI10.1016/0167-2789(84)90139-8zbMath0582.58016OpenAlexW1970067932MaRDI QIDQ1068400

Benno Fuchssteiner

Publication date: 1984

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: http://nbn-resolving.de/urn:nbn:de:hbz:466:2-1311

zbMATH Keywords

complete integrabilityLandau-Lifshitz equationPoisson structuresconstants of motionBenjamin-Ono and Kadomtsev-Petviashvili equationsspin waves in an anisotropic ferromagenet

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (10)

Nonlocal symmetries and recursion operator of the Landau–Lifshitz equation ⋮ The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links ⋮ New hierarchies of nonlinear completely integrable systems related to a change of variables for evolution parameters ⋮ Master Symmetries and Similarity Equations of theXYhModel ⋮ Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation laws ⋮ Representations of \(\mathfrak{sl}(2,\mathbb{C})\) in category \(\mathcal{O}\) and master symmetries ⋮ Symmetries and Integrability ⋮ The non-autonomous YdKN equation and generalized symmetries of Boll equations ⋮ Integrable generalizations of Schrödinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces ⋮ A new approach to the quantum KdV.

Cites Work

• Partition function of the eight-vertex lattice model
• The Lie Algebra Structure of Nonlinear Evolution Equations Admitting Infinite Dimensional Abelian Symmetry Groups
• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations

This page was built for publication: On the hierarchy of the Landau-Lifshitz equation