Principal results

• The new (direct) approach to the problem of variable separation in linear PDEs has been worked out. It is easily modified to become applicable to nonlinear PDEs as well (see the items B-20,29,40 of the Publication list ).
• Classification of (1+1)-dimensional wave equations with time-independent potentials that are solvable by separation of variables (see the items B-18,22 of the Publication list ).
• Complete classification of separable Kramers (Fokker-Plank type) equations (see the item B-50 of the Publication list ).
• Complete classification of separable (1+2)- and (1+3)-dimensional Schroedinger equations for a particle interacting with electro-magnetic field (see the items A-2; B-29,40,47,55 of the Publication list ).