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Completely integrable Hamiltonian systems connected with semisimple Lie algebras

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References

  1. Arnold, V.I.: Mathematical methods of classical mechanisms. Moscow, 1974 (in Russian)

  2. Moser, J.: Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math.16, 197 (1975).

    Google Scholar 

  3. Calogero, F.: Solution of the one-dimensionaln-body problems with quadratic and/or inversly quadratic pair potentials. J. Math. Phys.12, 419–436 (1971)

    Google Scholar 

  4. Sutherland, B.: Exact results for a quantum many-body problem in one dimension. II. Phys. Rev.A5, 1372–1376 (1972)

    Google Scholar 

  5. Lax, P. D.: Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math.21, 467–490 (1968)

    Google Scholar 

  6. Calogero, F., Marchioro C., Ragnisco, O.: Exact solution of the classical and quantal one-dimensional many-body problems with the two-body potentialV α(x)=g 2 a 2/sinh2 a x. Lett. Nuovo Cim.13, 383–387 (1975)

    Google Scholar 

  7. Calogero, F.: Exactly solvable one-dimensional many-body problems. Lett. Nuovo Cim.13, 411–416 (1975)

    Google Scholar 

  8. Bourbaki, N.: Groupes et algebras de Lie, Chapitres 4 5 et 6. Paris: Hermann 1969

    Google Scholar 

  9. Olshanetsky, M. A., Perelomov, A. M.: Completely integrable classical systems connected with semisimple Lie algebras. I. Lett. Math. Phys. (1976)

  10. Perelomov, A. M.: Completely integrable classical systems connected with semisimple Lie algebras. II. Preprint ITEP No. 27 (1976)

  11. Adler, M.: A New Integrable System and a Conjecture by Calogero. Preprint (1975)

  12. Bateman, H., Erdélyi, A.: Higher transcendental functions, v. 3, N. Y. 1955

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Olshanetsky, M.A., Perelomov, A.M. Completely integrable Hamiltonian systems connected with semisimple Lie algebras. Invent Math 37, 93–108 (1976). https://doi.org/10.1007/BF01418964

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