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Integrable Evolution Equations on Associative Algebras

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Abstract:

This paper surveys the classification of integrable evolution equations whose field variables take values in an associative algebra, which includes matrix, Clifford, and group algebra valued systems. A variety of new examples of integrable systems possessing higher order symmetries are presented. Symmetry reductions lead to an associative algebra-valued version of the Painlevé transcendent equations. The basic theory of Hamiltonian structures for associative algebra-valued systems is developed and the biHamiltonian structures for several examples are found.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.¶E-mail: olver@ima.umn.edu, http://www.math.umn.edu/∼olver, , , , , , US

    Peter J. Olver

  2. Ufa Mathematical Institute, Russian Academy of Sciences, Chernyshevski str. 112, 450000, Ufa, Russia. E-mail: sokolov@imat.rb.ru, , , , , , RU

    Vladimir V. Sokolov

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  1. Peter J. Olver
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  2. Vladimir V. Sokolov
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Received: 12 March 1997 / Accepted: 27 August 1997

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Olver, P., Sokolov, V. Integrable Evolution Equations on Associative Algebras . Comm Math Phys 193, 245–268 (1998). https://doi.org/10.1007/s002200050328

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  • DOI: https://doi.org/10.1007/s002200050328

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