## Integrable Evolution Equations on Associative Algebras (1997)

by
Peter J. Olver
,
Vladimir V. Sokolov

Citations: | 40 - 7 self |

### BibTeX

@MISC{Olver97integrableevolution,

author = {Peter J. Olver and Vladimir V. Sokolov},

title = {Integrable Evolution Equations on Associative Algebras },

year = {1997}

}

### OpenURL

### 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.