Duality, Solitons and Hydrodynamics in Generalized Calogero Models
Alexios Polychronakos (The City College and Graduate Center of the CUNY, New York)
I will present a first-order formulation of the Calogero model in external potentials in terms of a generating function, which simplifies the derivation of its dual form. Solitons naturally appear in this formulation as particles of negative mass. Using this method I derive the dual form of Calogero particles in external quartic, trigonometric and hyperbolic potentials, which were known to be integrable but had no known dual formulation. I will also derive the fluid mechanical formulation of these models and outline the corresponding fluid mechanical soliton solutions.