DYNAMICS OF THE INTERACTION OF TWO-DIMENSIONAL DOMAIN WALLS WITH A TOPOLOGICAL VORTEX

A numerical investigation of the dynamics of three-soliton interactions of 180-degree domain walls with a topological vortex (soliton) of the Belavin-Polyakov type in the phase space of a (2+1)- dimensional anisotropic O(3) invariant nonlinear sigma model is carried out. Models of interaction of topological structures of the kink-vortex-antikink type are obtained, where the annihilation of domain walls and complete decay of topological vortices onto localized perturbations that have a unit value of the Kronecker index are observed. It is established that in the case of the opposite direction of the field, the annihilating domain walls absorb some of the energy of the topological vortex equivalent to the unit value of the Kronecker index. In the case of domain walls of the same polarity, depending on the Bloch or Neel structure of the interphase boundaries, the process of their annihilation occurs, respectively, without absorbing the energy of the topological vortex or with energy absorption equivalent to the value of two units of the Kronecker index. Based on the methods of the theory of finite difference schemes and the application of the properties of stereographic projection, a complex program module is proposed that implements an algorithm for the numerical calculation of the evolution of three-soliton interactions in a stratified space.

Keywords:
three-soliton interaction, topological vortex, domain wall, nonlinear sigma-model, numerical simulation, stratified space.
УДК 519.6 + 530.1

DYNAMICS OF THE INTERACTION OF TWO-DIMENSIONAL DOMAIN WALLS WITH A TOPOLOGICAL VORTEX