Soliton stability in the O(3) sigma -model in (2+1) dimensions

The authors consider the instanton solutions of the O(3) sigma -model in two Euclidean dimensions as static solitons of the same model in (2+1) dimensions, and study their stability. Most of the work is numerical, based on two very different numerical procedures. On an infinite plane they find that such a soliton is, in general, unstable under small perturbations. It may either expand or contract, depending on the exact form of the initial disturbance. However, when the model is restricted to a finite region the boundary conditions can stabilise the soliton. They discuss these effects and their dependence on the initial conditions.