Nonlinear excitations in 1D ferromagnetic spin chains with anisotropic interactions

Nonlinear solitary-like and periodic-like excitations in a spin chain with a biquadratic anisotropic exchange interaction are investigated using coherent-state method combined with the Holstein–Primakoff bosonic representation of the spin operators. Using the idea of the shallow water wave approximation it has been shown that the modified terms of nonlinear Schrödinger equation are strongly restricted by the relation between the continuum approximation and the semi classical approximation. These relations may lead to three classes of the nonlinear Schrödinger equations. We derive solitary as well as the periodic solutions for each type of nonlinear Schrödinger-like equation for such a ferromagnetic chain.