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The Euler-Jacobi-Lie integrability theorem. (English) Zbl 1283.34035
This article deals with a class of problems associated with the conditions for exact integrability of ordinary differential equation systems expressed in terms of the properties of tensor invariants. There is proved a general theorem on the integrability of a system of \(n\) differential equations, which admits \(n-2\) independent symmetry fields and an invariant volume \(n\)-form. The obtained results are applied to some problems of magneto-hydrodynamics.

34C14 Symmetries, invariants of ordinary differential equations
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