Using the similarity ansatz, we have succeeded in constructing models with exactly known solutions, which makes it possible to consider systematically quantum corrections. The example of the model (28) demonstrates the inadequacy of the traditional form-factor expansion method. The restrictions on the parameters of the problem imposed by the ansatz can be lifted by means of perturbation theory, and in this sense the obtained solutions are reference solutions. A characteristic feature of problems of a particle in a field is the absence of a direct correlation between the parameter of the series expansion with respect to the dynamical variables and the value of the energy in the leading order, i. e., a large classical solution by no means necessarily leads to a large energy of the system. It would be interesting to investigate the mechanism of evolution of the solution in the case of vacuum degeneracy at the quantum level, and also to find a basis of asymptotic states over slowly decreasing solutions of massless fields. We hope to return to these questions. Note that the stability of our solutions must be considered in the complete scheme of collective coordinates, in which it is equivalent to positive definiteness of the form of the quantum fluctuations.