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Complex Deformation of Integrable Hamiltonians over Generalized Jacobi Varieties

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Nonlinear Processes in Physics

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Abstract

A class of algebraic and nonalgebraic completely integrable Hamiltonian systems defined on the symplectic manifolds is constructed. In particular, the meromorphic systems over the generalized Jacobians of the Riemann surfaces are considered in both scalar and matrix cases. Non-canonical action-angle variables are used to linearize the corresponding Hamiltonian flows and to establish the commutativity of the obtained finite (or infinite) collections of the integrable Hamiltonian systems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Nevada, Reno, NV, 89557, USA

    S. J. Alber

Authors
  1. S. J. Alber
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Editor information

Editors and Affiliations

  1. Clarkson University, 13699-5815, Potsdam, NY, USA

    A. S. Fokas  & D. J. Kaup  & 

  2. University of Arizona, 85721, Tucson, AZ, USA

    A. C. Newell  & V. E. Zakharov  & 

  3. Landau Institute for Theoretical Physics, ul. Kosygina 2, 117334, Moscow, Russia

    V. E. Zakharov

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© 1993 Springer-Verlag Berlin Heidelberg

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Alber, S.J. (1993). Complex Deformation of Integrable Hamiltonians over Generalized Jacobi Varieties. In: Fokas, A.S., Kaup, D.J., Newell, A.C., Zakharov, V.E. (eds) Nonlinear Processes in Physics. Springer Series in Nonlinear Dynamics . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77769-1_2

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  • DOI: https://doi.org/10.1007/978-3-642-77769-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77771-4

  • Online ISBN: 978-3-642-77769-1

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