The Euler-Jacobi-Lie integrability theorem (Q381020)

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.