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On Asymptotic Higher Analogs of the Helicity Invariant in Magnetohydrodynamics

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Abstract

We introduce a new asymptotic invariant of magnetic fields, namely, the quadratic (and polynomial) helicity. We construct a higher asymptotic invariant of a magnetic field. We also discuss various problems that can be solved by using the magnetic helicity invariant.

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Authors and Affiliations

  1. Institute of Geoagnetism, the Ionosphere, and Radiowave Propagation of the Russian Academy of Sciences, Moscow, Russia

    P. M. Akhmet’ev

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  1. P. M. Akhmet’ev
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Correspondence to P. M. Akhmet’ev.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 85, Proceedings of the International Conference on Differential Equations and Dynamical Systems (Suzdal, June 26–July 2, 2008), 2012.

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Akhmet’ev, P.M. On Asymptotic Higher Analogs of the Helicity Invariant in Magnetohydrodynamics. J Math Sci 200, 12–25 (2014). https://doi.org/10.1007/s10958-014-1900-5

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  • DOI: https://doi.org/10.1007/s10958-014-1900-5

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