Approximate second quantization method in the theory of quantum crystals

Nonideal and nonhomogeneous quantum Bose-systems are investigated by means of the Bogoliubov method of canonical transformation. For body-centered cubic crystal corresponding to the regular tetrahedron in the momentum space, three types of sound excitations are obtained. The interaction between the modes is of the next order with respect to the dimensionless momentum, as compared with the energy of elementary excitation.