Title: The structure of rationally factorized Lax type flows and their analytical integrability,
Abstract: The work is devoted to constructing a wide class of differential-functional
dynamical systems, whose rich algebraic structure makes their integrability
analytically effective. In particular, there is analyzed in detail the operator
Lax type equations for factorized seed elements, there is proved an important
theorem about their operator factorization and the related analytical solution
scheme to the corresponding nonlinear differential-functional dynamical
systems.