On the scattering theory of the classical hyperbolic Cn Sutherland model

In this paper, we study the scattering theory of the classical hyperbolic Sutherland model associated with the Cn root system. We prove that for any values of the coupling constants the scattering map has a factorized form. As a byproduct of our analysis, we propose a Lax matrix for the rational Cn Ruijsenaars-Schneider-van Diejen model with two independent coupling constants, thereby setting the stage to establish the duality between the hyperbolic Cn Sutherland and the rational Cn Ruijsenaars-Schneider-van Diejen models.