Geodesic
Asymptotics of the Spectrum and Eigenfunctions of the Magnetic Induction Operator on a Compact Two-Dimensional Surface of Revolution
Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 417-432

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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, turning point, WKB asymptotics
Mots-clés : quantization conditions, monodromy matrix. 
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     author = {A. I. Esina and A. I. Shafarevich},
     title = {Asymptotics of the {Spectrum} and {Eigenfunctions} of the {Magnetic} {Induction} {Operator} on a {Compact} {Two-Dimensional} {Surface} of {Revolution}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {417--432},
     publisher = {mathdoc},
     volume = {95},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a8/}
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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. Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 417-432. http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a8/