Stationary and moving breathers in (2+1)-dimensional O(3) nonlinear $\sigma$-model

TL;DR

This paper investigates the formation, stability, and dynamics of stationary and moving breather solutions in the (2+1)-dimensional O(3) nonlinear sigma model, combining analytical and numerical methods to explore their properties.

Contribution

It derives analytical oscillating solutions for the (2+1)-dimensional sine-Gordon equation and extends them to the O(3) sigma model, analyzing their long-term stability through numerical simulations.

Findings

Stationary and moving breathers remain stable over long periods.

Solutions exhibit weak radiation while maintaining stability.

Analytical solutions are successfully extended to the O(3) model.

Abstract

The formation and evolution of stationary and moving breather solutions in (2+1)-dimensional O(3) nonlinear $\sigma$-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 $\sigma$-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.