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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 199, Number 2, Pages 330–340
DOI: https://doi.org/10.4213/tmf9620 (Mi tmf9620) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Behavior of the solution of the Klein–Gordon equation with a localized initial condition

A. A. Tolchennikovab

a Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia
Full-text PDF (556 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf9620
Abstract: We consider the Klein–Gordon equation with a localized initial condition and describe the transition of the solution from localized to rapidly oscillating when the equation parameter changes.
Keywords: Klein–Gordon equation, localized initial condition.
Funding agency Grant number
Russian Science Foundation 16-11-10282
This research was supported by a grant from the Russian Science Foundation (Project No. 16-11-10282).
Received: 15.08.2018
Revised: 15.08.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 199, Issue 2, Pages 761–770
DOI: https://doi.org/10.1134/S0040577919050118
Bibliographic databases:
Document Type: Article
PACS: 02.30.Mv
MSC: 35B40
Language: Russian
Citation: A. A. Tolchennikov, “Behavior of the solution of the Klein–Gordon equation with a localized initial condition”, TMF, 199:2 (2019), 330–340; Theoret. and Math. Phys., 199:2 (2019), 761–770
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9620
  • https://www.mathnet.ru/eng/tmf/v199/i2/p330
    • This publication is cited in the following 3 articles:
    1. S.Yu. Dobrokhotov, E.S. Smirnova, “Asymptotics of the Solution of the Initial Boundary Value Problem for the One-Dimensional Klein–Gordon Equation with Variable Coefficients”, Russ. J. Math. Phys., 31:2 (2024), 187  crossref
    2. E. S. Smirnova, “Asymptotics of the Solution of an Initial–Boundary Value Problem for the One-Dimensional Klein–Gordon Equation on the Half-Line”, Math. Notes, 114:4 (2023), 608–618  mathnet  crossref  crossref
    3. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Russian Math. Surveys, 76:5 (2021), 745–819  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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