Soliton solutions of Calogero model in harmonic potential

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.

25 pages, 2 figures

References in corpus (9)

• Physics and Mathematics of Calogero particles
• Duality in Integrable Systems and Gauge Theories
• Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems
• Solitons in the Calogero-Sutherland Collective-Field Model
• Universal Wide Correlators in Non-Gaussian Orthogonal, Unitary and Symplectic Random Matrix Ensembles
• Semiclassical Approach to Finite-N Matrix Models

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• Lax random matrices from Calogero systems