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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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\pages 417--432
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    • This publication is cited in the following 5 articles:
    1. D.I. Borisov, D.M. Polyakov, “Uniform Spectral Asymptotics for a Schrödinger Operator on a Segment with Delta-Interaction”, Russ. J. Math. Phys., 31:2 (2024), 149  crossref
    2. A. A. Fedotov, “Complex WKB Method (One-Dimensional Linear Problems on the Complex Plane)”, Math Notes, 114:5-6 (2023), 1418  crossref
    3. Shafarevich A., “Quantization Conditions on Riemannian Surfaces and Spectral Series of Non-Selfadjoint Operators”, Formal and Analytic Solutions of Diff. Equations, Springer Proceedings in Mathematics & Statistics, 256, eds. Filipuk G., Lastra A., Michalik S., Springer, 2018, 177–187  crossref  mathscinet  isi
    4. A. A. Shkalikov, S. N. Tumanov, “Spectral Portraits in the Semi-Classical Approximation of the Sturm-Liouville Problem with a Complex Potential”, J. Phys.: Conf. Ser., 1141 (2018), 012155  crossref
    5. D. V. Nekhaev, A. I. Shafarevich, “A quasiclassical limit of the spectrum of a Schrödinger operator with complex periodic potential”, Sb. Math., 208:10 (2017), 1535–1556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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