arXiv subjects
Publications and source records attributed to F. Sh. Shokirov.
By numerical simulation methods the interactions of oscillating solutions (breathers) of the (2+1)-dimensional O(3) nonlinear sigma model is investigated. The models of head-on collisions in which the interacting breathers, in particular, are combined into a single oscillating soliton, the reflections from each other and pass through each other are obtained.
By methods of numerical simulation the interaction of 180-degree domain walls with oscillating solitons in (2+1)-dimensional O(3) nonlinear sigma model is investigated. A model of the collisions in which there is observed a reflection of solitons from each other, long-range interactions, as well as the decay of the oscillating soliton are obtained.
The formation and evolution of stationary and moving breather solutions in (2+1)-dimensional O(3) nonlinear $σ$-model are investigated. The analytical form of oscillating solutions for (2+1)-dimensional sine-Gordon equation, which evolve to periodic (breather) radially symmetric solutions is determined. On the basis of the found solutions by adding the rotations to the A3-field vector in isotopic space of S^2, the solutions for the O(3) nonlinear $σ$-model are obtained. By numerical study of the solutions dynamics their stability in a stationary and a moving state for quite a long time (45000 cycles), although in the presence of weak radiation is shown.
Dynamics of interaction of topological solitons (vortices) in (2+1)-dimensional O(3) nonlinear sigma model in anisotropic case are investigated. By numerical simulation methods is shown that the changes of rotation frequency of isotopic spin in the fiber space leads to an oscillatory dynamics of topological solitons. The models of interaction of oscillating topological solitons are obtained and their properties are investigated.
By methods of numerical simulations the dynamics of interaction of radially symmetric Bellavin-Polyakov type topological vortex in (2+1)-dimensional O(3) nonlinear sigma model is investigated. Obtained numerically the model of topological vortex decay for different values of radius of ring-shaped structure of their energy density onto the localized perturbations, where the sum of Hopf index is preserved. It is shown that the stability of topological solitons, in particularly, depends on the values of radius of ring-shaped structure of their energy density.