Soliton solutions of Calogero model in harmonic potential

Details Soliton solutions of Calogero model in harmonic potential Soliton solutions of Calogero model in harmonic potential

2011-03-31

arxiv.org/abs/1103.6231v1

J. Phys. A: Math. Theor. 44 (2011) 295203

Physics

Condensed Matter

Strongly Correlated Electrons

25 pages, 2 figures

Scientific paper

10.1088/1751-8113/44/29/295203

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 "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.

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