The method of moments of the Wigner distribution function is applied t
o the study of 1- collective excitations of atomic nuclei using Skyrme
type interactions. A set of dynamic equations describing the time evo
lution of compressible nucleus characteristics is derived which yields
seven energy levels, Some of them can be excited by multipole operato
rs: the corresponding excitation energies and fractions of the energy
weighted sum rules are compared to experimental data.