Interaction of a nonlinear spin-wave and magnetic soliton in a uniaxial anisotropic ferromagnet

We study the interaction of a nonlinear spin-wave and magnetic soliton in a uniaxial anisotropic ferromagnet. By means of a reasonable assumption and a straightforward Darboux transformation one- and two-soliton solutions in a nonlinear spin-wave background are obtained analytically, and their properties are discussed in detail. On the background of a nonlinear spin-wave the amplitude of the envelope soliton has the spatial and temporal period, and soliton can be trapped only in space. The amplitude and wave number of spin-wave have the different contribution to the width, velocity, and amplitude of soliton solutions. The envelope of solution hold the shape of soliton, and the amplitude of each envelope soliton keeps invariability before and after collision which shows the elastic collision of two envelope soliton on the background of a nonlinear spin-wave.