Dynamics of interaction of Bloch type domain walls in a two-dimensional nonlinear sigma model

Numerical simulation of the interaction of 180-degree Bloch-type domain walls in the phase space of the (2+1)-dimensional supersymmetric O(3) nonlinear sigma model is carried out. The method of numerical calculations is based on the special application of the properties of stereographic projection, where the projection of the isosphere onto the complex plane eliminates the problem of infinitely large quantities arising in the ordinary projection. Thus, the parametrization of the model under study in a complex form, necessary for the numerical approach, is realized, in which the singularity arising at the poles of the isosphere is overcome. A three-layer explicit difference scheme of the second order of accuracy with respect to time and coordinate on a five-point template is used. A complex programme module is proposed that implements the algorithm for the numerical calculation of space-time topological structures in three-dimensional lattices. The models of frontal collisions are obtained, where, depending on the dynamic parameters, processes of formation of bound (bion) states of domain walls, long-range models, passage of domain walls of magnetic domains through each other, as well as the formations of radially symmetric breathers are observed.