Scattering of periodic solitons

With the help of numerical simulations we study N-soliton scattering (N=3,4) in the (2+1)-dimensional CP^1 model with periodic boundary conditions. When the solitons are scattered from symmetrical configurations the scattering angles observed agree with the earlier \pi/N predictions based on the model on R_2 with standard boundary conditions. When the boundary conditions are not symmetric the angles are different from \pi/N. We present an explanation of our observed patterns based on a properly formulated geodesic approximation.