Soliton excitations in the alternating ferromagnetic Heisenberg chain

Soliton excitations in the alternating ferromagnetic Heisenberg spin chain are investigated with the use of the coherent-state method combined with the Holstein-Primakoff bosonic representation of spin operators. When the Hamiltonian and the equations of motion are recast in dimensionless forms, we obtain two partial differential equations with nonlinear coupling. Their nonlinear modified terms are strongly restricted by two dimensionless small parameters that are used in the semiclassical approximation and in the long-wavelength approximation. With use of the method of multiple scales, these equations are reduced to the nonlinear Schr\"odinger equation, which describes the slow spatial components of the coherent-state amplitudes. The results show that solitonlike magnon localization and the two-magnon bound state are possible in the system. The possibility of observing a gap soliton in the alternating ferromagnetic Heisenberg chain is also discussed.