  In the present paper, quantization of a weakly nonideal Bose gas at zero
temperature along the lines of the well-known Bogolyubov approach is performed.
The analysis presented in this paper is based, in addition to the steps of the
original Bogolyubov approach, on the use of nonoscillation modes (which are
also solutions of the linearized Heisenberg equation) for recovering the
canonical commutation relations in the linear approximation, as well as on the
calculation of the first nonlinear correction to the solution of the linearized
Heisenberg equation which satisfies the canonical commutation relations at the
next order. It is shown that, at least in the case of free quasi-particles,
consideration of the nonlinear correction solves the problem of nonconserved
particle number, which is inherent to the original approach.
