Scattering of periodic solitons

Abstract

Through numerical simulations we study $N$-soliton scattering ($N$=3,4) in the ($2+1)$-dimensional $CP^1$ model with periodic boundary conditions. Solitons colliding from symmetrical configurations scatter at $\pi/N$, as observed in the usual model with standard boundary conditions. When the initial configurations are not symmetric the angles differ from $\pi/N$. We describe our observed patterns based on a properly formulated geodesic approximation.