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TMF, 2017, Volume 193, Number 3, Pages 409–433 (Mi tmf9322)  

This article is cited in 1 scientific paper (total in 1 paper)

Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics

A. Yu. Anikinabc, S. Yu. Dobrokhotovab, A. I. Klevinab, B. Tirozzid

a Ishlinskii Institute for Problems in Mechanics, RAS, Moscow, Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
c Bauman Moscow State Technical University, Moscow, Russia
d ENEA Centro Ricerche di Frascati, Frascati (Roma), Italy

Abstract: We propose a method for determining asymptotic solutions of stationary problems for pencils of differential (and pseudodifferential) operators whose symbol is a self-adjoint matrix. We show that in the case of constant multiplicity, the problem of constructing asymptotic solutions corresponding to a distinguished eigenvalue (called an effective Hamiltonian, term, or mode) reduces to studying objects related only to the determinant of the principal matrix symbol and the eigenvector corresponding to a given (numerical) value of this effective Hamiltonian. As an example, we show that stationary solutions can be effectively calculated in the problem of plasma motion in a tokamak.

Keywords: spectrum, semiclassical asymptotic behavior, plasma equation, tokamak.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00521
16-31-00339
This research is supported by the Russian Foundation for Basic Research (Grant Nos. 14-01-00521 and 16-31-00339).


DOI: https://doi.org/10.4213/tmf9322

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English version:
Theoretical and Mathematical Physics, 2017, 193:3, 1761–1782

Bibliographic databases:

Received: 16.12.2016
Revised: 22.06.2017

Citation: A. Yu. Anikin, S. Yu. Dobrokhotov, A. I. Klevin, B. Tirozzi, “Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics”, TMF, 193:3 (2017), 409–433; Theoret. and Math. Phys., 193:3 (2017), 1761–1782

Citation in format AMSBIB
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\paper Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics
\jour TMF
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\vol 193
\issue 3
\pages 409--433
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\elib{http://elibrary.ru/item.asp?id=30738034}
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\jour Theoret. and Math. Phys.
\yr 2017
\vol 193
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\pages 1761--1782
\crossref{https://doi.org/10.1134/S0040577917120042}
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    This publication is cited in the following articles:
    1. A. Yu. Anikin, S. Yu. Dobrokhotov, A. I. Klevin, B. Tirozzi, “Gausian packets and beams with focal points in vector problems of plasma physics”, Theoret. and Math. Phys., 196:1 (2018), 1059–1081  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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