Duality in a model integrable even in a box-like confinement: Multi-soliton solutions and field theory
Manas Kulkarni (International Centre for Theoretical Sciences, Bengaluru)
Models that remain integrable even in confining potentials are extremely rare and almost non-existent. Here, we consider the Hyperbolic Calogero (HC) model which remains integrable even in confining potentials (which has box-like shapes). We present a first-order formulation of the HC model in external confining potential. Using the rich property of duality, we find multi-soliton solutions of this confined integrable model. We demonstrate the dynamics of these multi-soliton solutions via brute-force numerical simulations. We study the physics of soliton collisions and quenching using numerical simulations. We have examined the motion of dual variables and found an analytic expression for the time period in a certain limit. We give the field description of this model and find analytical solutions for background (absence of solitons) in the large-N limit (which has the form of a table-top). Analytical expressions of soliton solutions have been obtained in the absence of confining potential. Our work is of importance to understand general features of trapped interacting particles that remain integrable and can be of relevance to the collective behaviour of trapped cold atomic gases.