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Soliton solutions of a Calogero model in a harmonic potential. (English) Zbl 1223.37080

Summary: 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 the 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.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q51 Soliton equations
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