Dynamics of the classical Heisenberg ferromagnet
Dynamical properties of a classical anisotropic Heisenberg ferromagnet are analyzed by means of the stereographic representation for spin variables. The Gilbert damping term is included, and the failure of the complex time rescaling to account for damped solutions is shown. It is argued that the stereographic projection approach allows for formulating the damped Heisenberg ferromagnet dynamics within the mixed canonical-dissipative method. Finally the Benjamin-Fair instability of the finite-amplitude spin waves in the anisotropic Heisenberg chain is discussed.