We have studied nonlinear excitations of a quasi-one-dimensional anisotropic Heisenberg model subject to an external magnetic field. We have particularly been interested in the situation where the Zeeman energy can be varied continuously as a function of the parameter r. Taking the continuum limit, we have been able to show that this magnetic system can be mapped approximately onto the one-dimensional deformable sine-Gordon model at extremely low temperatures. Two classes of implicit soliton solutions that depend on r are presented and the total density of kinks and antikinks are calculated at low temperatures.