Heisenberg fields in the vicinity of a classical solution

The method of quantization in the neighbourhood of the classical solution based on the direct perturbative solution of the Cauchy problem for Heisenberg field equations is considered after the example of non-linear scalar field models in two-dimensional space-time. Like in classical Bogolubov-Krylov method zero modes are shown to appear as a result of perturbative expansion of Bogolubov's operator-values argument of classical component. With the help of LSZ-procedure a complete investigation of the soliton sector asymptotic states is carried out in the lowest perturbative orders