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Magnetic-field-induced translation of domain walls (DWs) in nanowires and nanostripes is accompanied by oscillatory transformations of the structure of the DW if the field intensity exceeds the Walker breakdown value. Such transformations are analytically described with relevance to soft-magnetic nanostripes, where they are oscillations between a transverse DW, a vortex DW, and an antivortex DW. Two regimes of the stripe thicknesses separated by a critical length of macrospin approximation (of the order of tens of nanometers) are considered. A simple local approach to magnetostatics is used within which the presence of magnetostatic field is included at the stripe edges only via boundary conditions on the DW solutions to the Landau-Lifshitz-Gilbert equation. It enables description of the multi-vortex textures (DWs) in the regime of thick stripes for which validity of the analytical Thiele approach and micromagnetic simulation codes can be questionable because they use different time scales when evaluating magnetostatic and exchange fields. A method of qualitative description of the domain wall transformations in thinner than the critical length stripes is proposed.