Abstract
The definition of partial Π- separation of variables is given and a covariant description is carried out of nonparabolic equations which in some coordinate system admit separation of variables; to this end, commutative algebras of differential symmetry operators of the equation of no higher than second order are used. In particular, necessary and sufficient conditions for complete Π-separation of variables are formulated in covariant form with respect to arbitrary transformations of the independent variables.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 116–122, May, 1978.
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Shapovalov, V.N. Symmetry and separation of variables in a linear differential equation of second order. I. Soviet Physics Journal 21, 645–650 (1978). https://doi.org/10.1007/BF00890983
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DOI: https://doi.org/10.1007/BF00890983