The hyperbolic image Sutherland and the rational image Ruijsenaars–Schneider–van Diejen models: Lax matrices and duality Original Research Article

In this paper, we construct canonical action–angle variables for both the hyperbolic image Sutherland and the rational image Ruijsenaars–Schneider–van Diejen models with three independent coupling constants. As a byproduct of our symplectic reduction approach, we establish the action–angle duality between these many-particle systems. The presented dual reduction picture builds upon the construction of a Lax matrix for the image-type rational Ruijsenaars–Schneider–van Diejen model.