Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

Abstract

By stereographically projecting the spin vector onto a complex plane in the equations of motion for a continuum Heisenberg 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 system is discussed. Then, introducing an auxiliary parameter, the Lax equations for Darboux matrices are generated recursively. By choosing the constants, the Jost solutions are satisfied the corresponding Lax equations. The exact soliton solutions are investigated, then the total magnetic momentum and its z-component are obtained. These results show that the solitary waves depend essentially on two velocities which describe a spin configuration deviating from a homogeneous magnetization. The depths and widths of solitary waves vary periodically with time. The center of an inhomogeneity moves with a constant velocity, while the shape of soliton also changes with another velocity and this shape is not symmetrical with respect to the center. The total magnetic momentum and its z-component vary with time.