Communications in Mathematical Physics

, Volume 193, Issue 2, pp 245–268 | Cite as

Integrable Evolution Equations on Associative Algebras

  • Peter J. Olver
  • Vladimir V. Sokolov

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.

Keywords

Evolution Equation Integrable System Basic Theory Field Variable Associative Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Peter J. Olver
    • 1
  • Vladimir V. Sokolov
    • 2
  1. 1.School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.¶E-mail: olver@ima.umn.edu, http://www.math.umn.edu/∼olverUS
  2. 2.Ufa Mathematical Institute, Russian Academy of Sciences, Chernyshevski str. 112, 450000, Ufa, Russia. E-mail: sokolov@imat.rb.ruRU

Personalised recommendations