SOLITONS IN A UNIAXIAL ANISOTROPIC HEISENBERG SPIN CHAIN WITH GILBERTDAMPING IN AN EXTERNAL MAGNETIC-FIELD

Using the stereographic projection of the unit sphere of the spin fiel d onto a complex plane for the equations of motion in a uniaxial aniso tropic Heisenberg spin chain with Gilbert damping in an external magne tic field, the effect of the magnetic field for the integrability of t he system is discussed. The effect of the Gilbert damping is also anal yzed. Then, introducing an auxiliary parameter, the Lax equations for the Darboux matrices are generated recursively. The Jest solutions sat isfy the corresponding Lax equations if constants are suitably chosen. The exact soliton solutions are then investigated. These results show that the solitary waves depend essentially on two velocities that des cribe a spin configuration deviated from a homogeneous magnetization, while the depths and widths of surface of solitary waves vary periodic ally with time. The center of an inhomogeneity moves with a constant v elocity, while the shape of a soliton also changes with another consta nt velocity and it is not symmetrical with respect to the center. The z component of the total magnetic momentum and the total magnetic mome ntum vary with time. The asymptotic behavior of multisoliton solutions is also given.