HIERARCHY OF EQUATIONS OF MOTION FOR NONLINEAR COHERENT EXCITATIONS APPLIED TO MAGNETIC VORTICES

The shape of a solitonlike excitation in a nonintegrable system genera lly depends on the velocity and all higher-order time derivatives of t he position (X) over right arrow of the excitation. Using a sequence o f generalized traveling-wave Ansatze we derive a hierarchy of equation s of motion for (X) over right arrow. The type of excitation determine s on which levels the hierarchy can be truncated consistently: ''Gyrot ropic'' excitations are governed by odd-order equations, nongyrotropic ones by even-order equations. Examples for the latter case are kinks in one-dimensional models and planar vortices of the two-dimensional a nisotropic (easy-plane) Heisenberg model. The nonplanar vortices of th is model an the simplest gyrotropic example. For this last case we sol ve the Hamilton equations for a finite system with one vortex and free boundary conditions and calculate the parameters of the third-order e quation of motion, This equation yields trajectories which are a super position of two cycloids with different frequencies, which is in full agreement with computer simulations of the full many-spin model. Final ly we demonstrate that the additional effects from the fifth-order equ ation are negligible.