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In this paper, we construct canonical action-angle variables for both thehyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-vanDiejen models with three independent coupling constants. As a byproduct of oursymplectic reduction approach, we establish the action-angle duality betweenthese many-particle systems. The presented dual reduction picture builds uponthe construction of a Lax matrix for the BC(n)-type rationalRuijsennars-Schneider-van Diejen model.

The hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality