NONLINEAR DYNAMICS OF A CONTINUUM HEISENBERG SPIN CHAIN WITH AN ANISOTROPY AND AN EXTERNAL MAGNETIC-FIELD

By stereographically projecting the spin vector onto a complex plane i n the equations of motion for a continuum Heisenbeg spin chain with an anisotropy (an easy plane and an easy axis) and an external magnetic field, the effect of the magnetic field for integrability of the syste m is discussed. Then, introducing an auxiliary parameter, the Lax equa tions for Darboux matrices are generated recursively. By choosing the constants, the Jest solutions are satisfied the corresponding Lax equa tions. The exact soliton solutions are investigated, then the total ma gnetic momentum and its z-component are obtained. These results show t hat the solitary waves depend essentially on two velocities which desc ribe a spin configuration deviating from a homogeneous magnetization, The depths and widths of solitary waves vary periodically with time. T he center of an inhomogeneity moves with a constant velocity, while th e shape of soliton also changes with another velocity and this shape i s not symmetrical with respect to the center. The total magnetic momen tum and its z-component vary with time.