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Matematicheskie Zametki, 2014, Volume 95, Issue 3, Pages 417–432
DOI: https://doi.org/10.4213/mzm10424 (Mi mzm10424) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Asymptotics of the Spectrum and Eigenfunctions of the Magnetic Induction Operator on a Compact Two-Dimensional Surface of Revolution

A. I. Esinaab, A. I. Shafarevichcb

a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moskovskaya obl.
c M. V. Lomonosov Moscow State University
Full-text PDF (595 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm10424
Abstract: Magnetic fields in conducting liquids (in particular, magnetic fields of galaxies, stars, and planets) are described by the magnetic induction operator. In this paper, we study the spectrum and eigenfunctions of this operator on a compact two-dimensional surface of revolution. For large magnetic Reynolds numbers, the asymptotics of the spectrum is studied; equations defining the eigenvalues (quantization conditions) are obtained; and examples of spectral graphs near which these points are located are given. The spatial structure of the eigenfunctions is studied.
Keywords: magnetic induction operator, two-dimensional surface of revolution, spectral graph, Stokes line, Reynolds number, quantization conditions, turning point, WKB asymptotics, monodromy matrix.
Received: 19.04.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 3, Pages 374–387
DOI: https://doi.org/10.1134/S0001434614030092
Bibliographic databases:
Document Type: Article
UDC: 517.958.53
Language: Russian
Citation: A. I. Esina, A. I. Shafarevich, “Asymptotics of the Spectrum and Eigenfunctions of the Magnetic Induction Operator on a Compact Two-Dimensional Surface of Revolution”, Mat. Zametki, 95:3 (2014), 417–432; Math. Notes, 95:3 (2014), 374–387
Citation in format AMSBIB
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\paper Asymptotics of the Spectrum and Eigenfunctions of the Magnetic Induction Operator on a Compact Two-Dimensional Surface of Revolution
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\yr 2014
\vol 95
\issue 3
\pages 417--432
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\jour Math. Notes
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\issue 3
\pages 374--387
\crossref{https://doi.org/10.1134/S0001434614030092}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899675306}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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