On explicit solutions for completely integrable classical Calogero-Moser systems in external fields

TL;DR

This paper derives explicit solutions for specific Calogero-Moser systems with external fields, analyzing particle interactions and conditions leading to singularities, thereby advancing understanding of integrable classical systems.

Contribution

It provides explicit solutions for three and four particle Calogero-Moser systems in external fields, linking parameters to system behavior and singularity timing.

Findings

Explicit solutions for 3- and 4-particle systems

Relation between coupling constant, initial conditions, and singularity time

Conditions for particles falling into potential singularities

Abstract

Explicit solutions for one completely-integrable system of Calogero-Moser type in external fields are found in case of three and four interacting particles. Relation between coupling constant, initial values of coordinates and time of falling into the singularity of potential is derived.