Scattering theory of the hyperbolic BCn Sutherland and the rational BCn Ruijsenaars-Schneider-van Diejen models

In this paper, we investigate the scattering properties of the hyperbolic BC_n Sutherland and the rational BC_n Ruijsenaars-Schneider-van Diejen many-particle systems with three independent coupling constants. Utilizing the recently established action-angle duality between these classical integrable models, we construct their wave and scattering maps. In particular, we prove that for both particle systems the scattering map has a factorized form.