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)
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