Abstract
A covariant description of nonparabolic first-order partial differential equations such that separation of variables is possible in any coordinate system is given; this involves the use of the commutative Lie symmetry groups of the equations. In particular, the necessary and sufficient conditions for complete separation of variables are formulated in a form that is covariant with respect to arbitrary transformation of the independent variables.
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V. N. Shapovalov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5 (1978).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 18–24, September, 1978.
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Shapovalov, V.N. Symmetry and separation of variables in Hamilton-Jacobi equations. I. Soviet Physics Journal 21, 1124–1129 (1978). https://doi.org/10.1007/BF00894559
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DOI: https://doi.org/10.1007/BF00894559