Symmetry and separation of variables in second-order differential equations. II

A definition of the complete separation of variables is given, and normal parabolic equations permitting separation of variables in any coordinate system are described; this involves the commutative algebra of differential (not higher than second order) symmetry operators of the equations. In particular, the necessary and sufficient conditions for the complete n separation of variables is formulated in covariant form with respect to arbitrary transformations of the independent variables.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 7–10, June, 1978.