Reduced dynamics of Ward solitons

The moduli space of static finite energy solutions to Ward’s integrable chiral model is the space $M_N$ of based rational maps from ${\text{CP}}^1$ to itself with degree $N$. The Lagrangian of Ward’s model gives rise to a K"ahler metric and a magnetic vector potential on this space. However, the magnetic field strength vanishes, and the approximate non–relativistic solutions to Ward’s model correspond to a geodesic motion on $M_N$. These solutions can be compared with exact solutions which describe non–scattering or scattering solitons.