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Self-localized domain wall (DW) oscillations in a uniaxial ferromagnet in the presence of dissipation and a periodic homogeneous magnetic field are under investigation. On the basis of perturbation theory and the direct numerical solution of magnetodynamic equations, the stabilization conditions of soliton-like domain wall oscillations have been found. For a given frequency of pumping field, the narrow range of field magnitude, where the effects of self-organization on the domain wall appear, has been discovered. The threshold of the external field amplitude, when the generation of Bloch lines in the domain wall starts, has been obtained approximately. Such generation is the initial stage of chaotization of the domain wall under the parametric pump, which has been observed in the numerical experiments.