Completely integrable model of classical field theory with nontrivial particle interaction in two-dimensional space-time

The complete integrability of a nonlinear relativistic equation, being a generalization of the sine-Gordon equation for the case of group $SO(3)$, is shown. The soliton spectrum is described and exact solutions describing their interaction are obtained. It is shown that together with elastic scattering there exist the processes of decay and merging of solitons. A generalization of the sine-Gordon equation for an arbitrary compact Lie group is discussed.