Mathematical modeling of breathers of two-dimensional O(3) nonlinear sigma model

The study examined the formation and evolution of stationary and moving breathers of a two-dimensional O(3) nonlinear sigma model. We detected analytical form of trial functions of two-dimensional sine-Gordon equations, which over time evolve into periodic (breather) solutions. According to the solutions found, by adding the rotation to an A3-field vector in isotopic space $S^2$ we obtained the solutions for the O(3) nonlinear sigma model. Furthermore, we conducted the numerical study of the solutions dynamics and showed their stability in a stationary and a moving state for quite a long time, although in the presence of a weak radiation.