Heisenberg fields in the neighbourhood of classical solution

A method of quantization in the neighbourhood of classical solution based on the direct perturbation theory solution of the Cauchy problem for Heisenberg field equations is considered for the case of nonlinear scalar field models in two-dimensionalspace-time. It is shown that zero modes and secular terms related to them as in the classical Bogolyubov-Krylov method arise due to the series expansion of the Bogolyubov operator argument of the classical component. By means of LSZ-procedure the complete investigation of asymptotical states of the field in the soliton sector is performed in lower perturbation theory orders