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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm10424https://doi.org/10.4213/mzm10424 https://www.mathnet.ru/eng/mzm/v95/i3/p417
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Abstract page: | 494 | Full-text PDF : | 138 | References: | 73 | First page: | 43 |
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