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In this paper, we construct global action-angle variables for a certaintwo-parameter family of hyperbolic van Diejen systems. Following Ruijsenaars'ideas on the translation invariant models, the proposed action-angle variablescome from a thorough analysis of the commutation relation obeyed by the Laxmatrix, whereas the proof of their canonicity is based on the study of thescattering theory. As a consequence, we show that the van Diejen system of ourinterest is self-dual with a factorized scattering map. Also, in an appendix byS. Ruijsenaars, a novel proof of the spectral asymptotics of certainexponential type matrix flows is presented. This result is of crucialimportance in our scattering-theoretical analysis.

Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)