We investigate solitary excitations in a model of a one-dimensional antiferromagnet
including a single-ion anisotropy and a Dzyaloshinsky–Moriya antisymmetric exchange
interaction term. We employ the Holstein–Primakoff transformation, the coherent state
ansatz and the time variational principle. We obtain two partial differential equations of
motion by using the method of multiple scales and applying perturbation theory. By so
doing, we show that the motion of the coherent amplitude must satisfy the nonlinear
Schrödinger equation. We give the single-soliton solution.