Symmetry and separation of variables in a linear differential equation of second order. I
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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.
Keywords
Differential Equation Coordinate System Linear Differential Equation Commutative Algebra Covariant Form
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© Plenum Publishing Corporation 1978