The Euler–Jacobi–Lie integrability theorem

    2013, Vol. 9, No. 2, pp.  229-245

    Author(s): Kozlov V. V.

    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

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