Integral formula for a generalized Sato-Levine invariant in magnetic hydrodynamics
type: Item
instance of: scholarly article
title: Integral formula for a generalized Sato-Levine invariant in magnetic hydrodynamics
zbMATH Open document ID: 1190.53071
DOI: 10.1134/S0001434609030225
author: O. V. Kunakovskaya
author: Petr Akhmet'ev
published in: Mathematical Notes
publication date: 2009-11-10T00:00:00Z
review text: The authors investigate the problem of finding a higher analog of the helicity integral for divergence-free vector fields. They propose the construction of a new fourth-order integral \(\mathbf{W}\) which is defined for the magnetic field represented by two tubes, and extend a previous integral defined for two tubes with zero linking number [J. Geom. Phys. 15, No.~2, 95--101 (1995; Zbl 0836.57005)]. It is shown that \(\mathbf{W}\) is preserved under the motion of tubes in an ideal medium. Also, the topological meaning of \(\mathbf{W}\) is discussed and compared with the generalized Sato-Levine invariant.
reviewed by: Paolo Dulio
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 5628180
zbMATH Keywords: gradient field
zbMATH Keywords: Lie derivative
zbMATH Keywords: linking number
zbMATH Keywords: Massey product
zbMATH Keywords: magnetic hydrodynamics
zbMATH Keywords: oriented magnetic tube
zbMATH Keywords: Sato-Levine invariant
zbMATH Keywords: topological invariant
MaRDI profile type: Publication
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full work available at URL: s0001434609030225
OpenAlex ID: W1984618716
description: scientific article; zbMATH DE number 5628180