  The results of numerical simulation of the interaction of topological
solitons (2+1)-dimensional O(3) non-linear sigma model in reversed time are
presented. At the first stage, models of interactions of topological vortices
are developed, where, depending on the dynamic parameters, processes of their
decay into localized perturbations and phased annihilation are observed. Also,
models for the phased annihilation of topological vortices during their
interaction with 180-degree domain walls are considered. On the basis of the
models obtained, initial conditions for numerical simulation of interaction
processes in reversed time are developed. The models describing the complete
restoration of the initial topological field of interacting solitons at the
combination of localized perturbations and radiation waves are obtained. Also,
models are obtained that describe the formation of topological vortices in the
plane of the domain wall and their subsequent emission. Thus, the T-invariance
property of the field-theoretic model under study is confirmed. Numerical
calculations were carried out in a stratified space on the basis of methods of
the theory of finite difference schemes, using the properties of a
stereo-graphic projection. The experiments were carried out for different
values of the Kronecker-Hopf index of topological vortices. A complex program
module is proposed that implements a special algorithm for the numerical
calculation of the evolution of the interaction of space-time topological
structures in reversed time.

Pattern Formation and Solitons