Communications in Mathematical Physics

, Volume 115, Issue 1, pp 127–165

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

I. The pure soliton case
  • S. N. M. Ruijsenaars

DOI: 10.1007/BF01238855

Cite this article as:
Ruijsenaars, S.N.M. Commun.Math. Phys. (1988) 115: 127. doi:10.1007/BF01238855


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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • S. N. M. Ruijsenaars
    • 1
  1. 1.Centre for Mathematics and Computer ScienceAmsterdamThe Netherlands

Personalised recommendations