A THEOREM ON 2 COMMUTING AUTOMORPHISMS, AND INTEGRABLE DIFFERENTIAL-EQUATIONS

Constructions are found for differential equations in an arbitrary continuous associative algebra U that admit an equivalent Lax representation (with spectral parameter) in the space of linear operators acting on U. The constructions use commuting automorphisms of U. Applications of the main construction are indicated for the construction of integrable Euler equations in the direct sum of the Lie algebras gl(n, R) and so(n, R). Constructions are presented for matrix differential equations admitting a Lax representation with several spectral parameters.