  Dynamics of magnetic bubbles in planar ferromagnets described by the
Landau-Lifshitz equation with dissipation is analyzed. The pure O(3) sigma
model has static multisoliton solutions, characterized by a number of
parameters. The parameters describe a finite dimensional manifold. A small
perturbation of energy functional with respect to the sigma model forces
solitons to move. Multisoliton dynamics is effectively reduced to a flow in the
parameter space.
