THE ANALYTIC ASPECTS OF THE BOGOLIUBOV GENERATING FUNCTIONAL EQUATIONS WITHIN THE BOBOLIUBOV CANONICAL TRANSFORMATION METHOD Nikolai N. Bogolubov, Jr. V.A. Steklov Mathematical Institute of RAN, Moscow, Russia e-mail: nickolai bogolubov@hotmail.com Anatoliy K. Prykarpatsky The AGH University of Science and Technology Department of Applied Mathematics Krak´ ow 30059 Poland e-mail: prykanat@cybergal.com, pryk.anat@ua.fm (Received 27 February 2007; accepted 1 March 2007) Abstract The analytic aspects of the Bogoliubov generating func- tional equations and their transformation properties within the Bogoliubov canonical transformation method are studied. The classical Bogoliubov idea [2] to use the Wigner density operator transformation for studying the non equilibrium dis- tribution functions within the Bogoliubov canonical transfor- mation method is developed, a new analytic non-stationary solution to the classical N.N. Bogoliubov evolution functional equation is constructed. Concepts of Physics, Vol. IV, No. 3 (2007) DOI: 10.2478/v10005-007-0015-x 361