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Nonlinear Evolution Equations and Dynamical Systems pp 144–147Cite as

An Abstract Tri-Hamiltonian Lax Hierarchy

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Part of the book series: Research Reports in Physics ((RESREPORTS))

Abstract

Starting with an r-matrix on an associative algebra g equipped with a nondegenerate traceform three natural compatible Poisson brackets can be defined. The associated Hamiltonian equations turn out to be of Lax type. The Casimir functions on g are in involution w.r.t. all three brackets and lead to a hierarchy of tri-Hamiltonian evolution equations in Lax form. Wellknown examples of finite-dimensional integrable systems, integrable lattice equations as well as integrable PDE’s can be described in this framework.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Paderborn, D-4790, Paderborn, Fed. Rep. of Germany

    W. Oevel

  2. Dipartimento di Fisica, Università degli Studi di Roma “La Sapienza”, I-00185, Roma, Italy

    O. Ragnisco

Authors
  1. W. Oevel
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  2. O. Ragnisco
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Editor information

Editors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma „La Sapienza“, via A. Scarpa 10, I-00161, Roma, Italy

    Sandra Carillo

  2. Dipartimento di Fisica, Università di Roma „La Sapienza“, P. le A. Moro 2, I-00185, Roma, Italy

    Orlando Ragnisco

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© 1990 Springer-Verlag Berlin, Heidelberg

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Oevel, W., Ragnisco, O. (1990). An Abstract Tri-Hamiltonian Lax Hierarchy. In: Carillo, S., Ragnisco, O. (eds) Nonlinear Evolution Equations and Dynamical Systems. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84039-5_27

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  • DOI: https://doi.org/10.1007/978-3-642-84039-5_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51983-6

  • Online ISBN: 978-3-642-84039-5

  • eBook Packages: Springer Book Archive

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