Integrable Evolution Equations on Associative Algebras (1997)
by
Peter J. Olver
,
Vladimir V. Sokolov
| Citations: | 33 - 7 self |
BibTeX
@MISC{Olver97integrableevolution,
author = {Peter J. Olver and Vladimir V. Sokolov},
title = {Integrable Evolution Equations on Associative Algebras },
year = {1997}
}
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Abstract
This paper surveys the classi cation of integrable evolution equations whose eld 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 associative algebra-valued version of the Painleve transcendent equations. The basic theory of Hamiltonian structures for associative algebra-valued systems is developed and the bi-Hamiltonian structures for several examples are found.
