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Soliton solutions of Calogero model in harmonic potential

By Alexander G. Abanov, Andrey Gromov and Manas Kulkarni

Abstract

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.Comment: 25 pages, 2 figure

Topics: Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory, Mathematical Physics
Year: 2011
DOI identifier: 10.1088/1751-8113/44/29/295203
OAI identifier: oai:arXiv.org:1103.6231
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