CsMnBr3 is a quasi-one-dimensional antiferromagnetic insulator. The spin interactions are predominately of a Heisenberg nature, but at low temperatures the smaller dipolar interactions result in "easy-plane" one-dimensional antiferromagnetic ordering. We have examined the spin fluctuations at low energies, near the magnetic zone centre, with inelastic neutron scattering techniques. By means of a subtraction algorithm, we have separated intensities, as a function of the wave vector and energy, of the two polarizations of spin fluctuations (in-plane and out-of-plane). We report a strong qualitative difference between the energy dependence of the two polarizations, with the "out-of-plane" intensity exhibiting central-mode behaviour. A model of noninteracting Sine–Gordon solitons in the easy-plane antiferromagnet proposed by Mikeska provides an excellent qualitative and reasonable quantitative accounting of the polarization, wave vector, and energy dependence of the neutron scattering with low-energy transfer at 15 K. The model, however, cannot account for our elevated-temperature results. We have modified the theory using the phenomenological approach of ascribing an upwards renormalization of the soliton mass with temperature. The resulting comparison with our results is good.