Solitonlike structure in the parametric distortions of bounded-system energy spectra

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Abstract
Exact one-soliton and two-soliton solutions of generalized Calogero-Moser (gCM) equations are presented. We explain how these solutions describe the origin of the successive avoided crossings observed in the energy-level structure of bounded systems when a parameter is varied. A new statistical description, based on the grand-canonical ensemble for the gCM system, is developed for the study of the parametric properties of irregular spectra. The relationship with random matrix theory is discussed.