Siberian Federal University

For the case of a strong one-site boson repulsion the temperature of the Bose-condensation have been calculated when boson hopping take into account for three co-ordinating spheres. In the solution the task an indefinite metric method was applied to provide an exact bose-analog of the Hamil- tonian, written in the atomic representation. Through an unitary transformation the transition to a Hamiltonian with the break down global U(1) symmetry in the phase with condensate was realized. As this takes place the spectrum of excitations for small values of the quasimomentum has characteristics corresponding to the superfluid phase