Abstract
The Landau-Lifshitz equation (LL-equation) is shown to have infinitely many commuting one-parameter symmetry groups and constants of motion in involution. The infinitesimal generators of these one-parameter symmetry groups define the hierarchy of the LL-equation. We give explicit formulas for these generators and for the conserved densities. Furthermore, infinitely many time-dependent symmetry groups and conservation laws are constructed. All results are obtained via a simple direct Lie algebra approach and without making any use of the quantum inverse scattering method based on the ingenious results of R.J. Baxter.
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