No abstract

No abstract

No abstract

This paper surveys the classication of integrable evolution equations whose eld variables take v alues 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 Painlev e 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.

No abstract