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 spacelike plane in R2,1 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 quantised 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 classical energy quantisation of moving solitons. email [email protected] email [email protected] 1