Topology and energy of time-dependent unitons

We consider a class of time-dependent finite energy multi-soliton solutions of the U ( N ) integrable chiral model in (2+1) dimensions. The corresponding extended solutions of the associated linear problem have a pole with arbitrary multiplicity in the complex plane of the spectral parameter. Restrictions of these extended solutions to any space-like plane in have trivial monodromy and give rise to maps from a three-sphere to U ( N ). We demonstrate that the total energy of each multi-soliton is quantized at the classical level and given by the third homotopy class of the extended solution. This is the first example of a topological mechanism explaining the classical energy quantization of moving solitons.