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Matematicheskie Zametki, 2012, Volume 92, Issue 2, Pages 163–180
DOI: https://doi.org/10.4213/mzm9749 (Mi mzm9749) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators

J. Brüninga, V. V. Grushinbc, S. Yu. Dobrokhotovdc

a Humboldt University, Germany
b Moscow State Institute of Electronics and Mathematics
c Moscow Institute of Physics and Technology
d A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
Full-text PDF (627 kB) Citations (15)
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DOI: https://doi.org/10.4213/mzm9749
Abstract: An example of Schrödinger and Klein–Gordon equations with fast oscillating coefficients is used to show that they can be averaged by an adiabatic approximation based on V. P. Maslov's operator method.
Keywords: Klein–Gordon equation, Schrödinger equation, adiabatic approximation, asymptotic solution, pseudodifferential operator, adiabatic principle, perturbation theory.
Received: 28.12.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 2, Pages 151–165
DOI: https://doi.org/10.1134/S0001434612070188
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: J. Brüning, V. V. Grushin, S. Yu. Dobrokhotov, “Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators”, Mat. Zametki, 92:2 (2012), 163–180; Math. Notes, 92:2 (2012), 151–165
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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