Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. II. Solitons, Antisolitons, and their Bound States | Zendy

S. N. M. Ruijsenaars | Zendy

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Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. II. Solitons, Antisolitons, and their Bound States

Author(s) -

S. N. M. Ruijsenaars

Publication year - 1994

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195164945

Subject(s) - integrable system , mathematics , action (physics) , scattering , mathematical physics , bound state , pure mathematics , physics , quantum mechanics

We construct an action-angle transformation for the CalogeroMoser systems with repulsive potentials, and for relativistic generalizations thereof. This map is shown to be closely related to the wave transformations for a large class ^ of Hamiltonians, and is shown to have remarkable duality properties. All dynamics in ̂ 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 form M exp(ίD) as ί-> oo. It pertains to diagonal matrices D whose diagonal elements have pairwise different real parts and to matrices M for which certain principal minors are non-zero. Table of

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