semiclassical description of anisotropic non-heisenberg magnets for spin s=1 and linear quadrupole excitation dynamics

in this paper, lagrangian and equations describing one-dimensional anisotropic non-heisenberg model are studied. in this study we used the generalized coherent states in real parametrizations and the feynman path integral for these states in su(3) group. these equations describe nonlinear dynamics of non-heisenberg ferromagnetic chain completely. solutions of these equations are magnetic solitons, (that are not studied in this paper).these equations shown that for anisotropic ferromagnets, the magnitude of average quadruple moment (excitation) is not constant and its dynamics consists of two parts. one part is rotational dynamics around the classical spin vector and the other related to change of magnitude of quadruple moment. then dissipative spin wave equation for dipole and quadruple branches is obtained if there is a small linear excitation in the ground (vacuum) state. these equations show that both dipole and quadrupole branches in su(3) group in the hamiltonian (1) in this problem are dispersion.