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.
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Simon N. M. Ruijsenaars, Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. II. Solitons, Antisolitons, and their Bound States. Publ. Res. Inst. Math. Sci. 30 (1994), no. 6, pp. 865–1008DOI 10.2977/PRIMS/1195164945