Soliton Solution for the Spin Current in Ferromagnetic Nanowire

We investigate the interaction of a periodic solution and one-soliton solution for the spin-polarized current in a uniaxial ferromagnetic nanowire. The amplitude and wave number of the periodic solution for the spin current have the different contribution to the width, velocity, and the amplitude of soliton solution, respectively. Moreover, we found that the soliton can be trapped only in space with a proper condition. At last we analyze the modulation instability and discuss dark solitary wave propagation for the spin current on the background of a periodic solution. In some special cases the solution can be expressed by the linear combination of periodic solution and soliton solution.