Integrable evolution equations on associative algebras

Peter J. Olver, Vladimir V. Sokolov

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121 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)245-268
Number of pages24
JournalCommunications in Mathematical Physics
Volume193
Issue number2
DOIs
StatePublished - Apr 3 1998

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