Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. II. Solitons, Antisolitons, and their Bound States

Abstract

We present an explicit construction of an action-angle map for the nonrelativistic Calogero-Moser systems with 1/sh2 and —1/ch2 pair potentials, and for relativistic generalizations thereof. The map is used to obtain extensive information concerning dynamics and scattering. We also discuss the relation between the relativistic N-particle systems and the N-particle-like solutions of various soliton PDEs, including the sine-Gordon equation.