We argued that the standard field scalar potential couldn't be widely used for getting the adequate galaxies' curve lines and determining the profiles of dark matter their halo. For discovering the global properties of scalar fields that can describe the observable characteristics of dark matter on the cosmological space and time scales, we propose the simplest form of central symmetric potential celestial - mechanical type, i.e. U(ϕ) = -μ/ϕ. It was shown that this potential allows get rather satisfactorily dark matter profiles and rotational curves lines for dwarf galaxies. The good agreement with some previous results, based on the N-body simulation method, was pointed out. A new possibility of dwarf galaxies' masses estimation was given, also.

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