Nonlinear excitations in the classical one-dimensional antiferromagnet

In this paper we study nonlinear excitations in the classical one-dimensional antiferromagnet with two anisotropies and an external magnetic field with components parallel and perpendicular to the chain. We use the continuum approximation, at low temperatures, to obtain two coupled nonlinear equations in the variables theta and Φ, and then we discuss some limit solutions to these equations. We study the equivalence of this model, from the thermodynamical point of view, to an anisotropic ferromagnet whose statistical mechanics has been studied in the literature. We then use this equivalence to calculate the inverse correlation length, the neutron scattering intensity integrated over energy, the soliton density, and the soliton energy. Our theory is found to be in good agreement with experimental data for tetramethyl ammonium trichloride [TMMC,(${\mathrm{CD}}_3$ ${)}_4$ ${\mathrm{NMnCl}}_3$].