Soliton scattering in the Skyrme model in (2+1) dimensions. I. Soliton-soliton case

Abstract

The authors consider instanton and anti-instanton solutions of the O(3) sigma -model in two Euclidean dimensions modified by the addition of an appropriate potential and Skyrme-like terms as static solitons (and antisolitons) of the same model in (2+1) dimensions. They study various scattering properties of these structures, which they call skyrmions. Most of the work is numerical and uses two formulations of the model; the well-known formulation in terms of a real vector field phi (with three components restricted to phi . phi =1) and the formulation involving one complex field. They compare their results with similar results obtained in the pure O(3) sigma -model. They find that the potential and Skyrme terms which stabilize the skyrmions have relatively little effect on their scattering properties. In the scattering process initiated at low relative velocities the skyrmions bounce back while at velocities larger than some critical value they scatter at right angles. The value of this critical velocity depends on the values of the parameters of the potential and skyrme terms. The scattering is quasi-elastic and the skyrmions preserve their shape after the collision. They also analyse the scattering properties of rotating skyrmions and present their trajectories for some values of their rotation for several values of the parameters of the additional terms.