Communications in Mathematical Physics

, Volume 115, Issue 1, pp 127-165

First online:

Action-angle maps and scattering theory for some finite-dimensional integrable systems

I. The pure soliton case
  • S. N. M. RuijsenaarsAffiliated withCentre for Mathematics and Computer Science

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We construct an action-angle transformation for the Calogero-Moser systems with repulsive potentials, and for relativistic generalizations thereof. This map is shown to be closely related to the wave transformations for a large classl of Hamiltonians, and is shown to have remarkable duality properties. All dynamics inl lead to the same scattering transformation, which is obtained explicitly and exhibits a soliton structure. An auxiliary result concerns the spectral asymptotics of matrices of the formM exp(tD) ast→∞. It pertains to diagonal matricesD whose diagonal elements have pairwise different real parts and to matricesM for which certain principal minors are non-zero.