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