This paper addresses a class of problems associated with the conditions for exact integrability of a system of ordinary differential equations expressed in terms of the properties of tensor invariants. The general theorem of integrability of the system of $n$ differential equations is proved, which admits $n − 2$ independent symmetry fields and an invariant volume $n$-form (integral invariant). General results are applied to the study of steady motions of a continuous medium with infinite conductivity.
Keywords:
symmetry field, integral invariant, nilpotent group, magnetic hydrodynamics
Citation:
Kozlov V. V., The Euler–Jacobi–Lie integrability theorem, Rus. J. Nonlin. Dyn.,
2013, Vol. 9, No. 2,
pp. 229-245
DOI:10.20537/nd1302003