Abstract |

**On Some Class of Factorized Dynamical
Systems and Their Integrability**

*A.K.Prykarpatsky, R.Basiura (Department
of Applied Mathematics at the University of Mining and Metallurgy, Krakow,
Poland)*

*e-mail:
prykanat@cybergal.com,prikarpa@mat.agh.edu.pl*

There
is studied the algebraic structure of a class of operatorial evolution
equations factorizing standard Lax type integrable flows on the adjoint space
to a Lie algebra of pseudo-differential operators. We found the corresponding
Poisson structure on the corresponding subgroup Lie, constructed an infinite
hierarchy of conservation laws. Some
interesting applications to Korteweg-de Vries type dynamical systems are
attached.

Section
: 12