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

I. The pure soliton case

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Abstract

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.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, NL-1009 AB, Amsterdam, The Netherlands

    S. N. M. Ruijsenaars

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  1. S. N. M. Ruijsenaars
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Communicated by J. Mather

Work supported by the Netherlands Organisation for the Advancement of Pure Research (ZWO)

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Ruijsenaars, S.N.M. Action-angle maps and scattering theory for some finite-dimensional integrable systems. Commun.Math. Phys. 115, 127–165 (1988). https://doi.org/10.1007/BF01238855

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  • DOI: https://doi.org/10.1007/BF01238855

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