Soliton solutions of a Calogero model in a harmonic potential

A classical Calogero model in an external harmonic potential is known to be integrable for any number of particles. We consider here reductions which play a role of the 'soliton' solutions of the model. We obtain these solutions both for the model with finite number of particles and in a hydrodynamic limit. In the latter limit, the model is described by hydrodynamic equations on continuous density and velocity fields. Soliton solutions in this case are finite-dimensional reductions of the hydrodynamic model and describe the propagation of lumps of density and velocity in the nontrivial background.