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Sbornik: Mathematics, 2010, Volume 201, Issue 12, Pages 1731–1775
DOI: https://doi.org/10.1070/SM2010v201n12ABEH004129
(Mi sm7583)
 

This article is cited in 8 scientific papers (total in 8 papers)

Quasitravelling waves

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS
References:
Abstract: A finite difference analogue of the wave equation with potential perturbation is investigated, which simulates the behaviour of an infinite rod under the action of an external longitudinal force field. For a homogeneous rod, describing solutions of travelling wave type is equivalent to describing the full space of classical solutions to an induced one-parameter family of functional differential equations of point type, with the characteristic of the travelling wave as parameter. For an inhomogeneous rod, the space of solutions of travelling wave type is trivial, and their ‘proper’ extension is defined as solutions of ‘quasitravelling’ wave type. By contrast to the case of a homogeneous rod, describing the solutions of quasitravelling wave type is equivalent to describing the quotient of the full space of impulsive solutions to an induced one-parameter family of point-type functional differential equations by an equivalence relation connected with the definition of solutions of quasitravelling wave type. Stability of stationary solutions is analyzed.
Bibliography: 9 titles.
Keywords: functional differential equations, scale of function spaces, impulsive solutions, wave equation, travelling waves.
Received: 08.06.2009 and 02.06.2010
Bibliographic databases:
Document Type: Article
UDC: 517.927.4
MSC: Primary 34K31; Secondary 74C99
Language: English
Original paper language: Russian
Citation: L. A. Beklaryan, “Quasitravelling waves”, Sb. Math., 201:12 (2010), 1731–1775
Citation in format AMSBIB
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\by L.~A.~Beklaryan
\paper Quasitravelling waves
\jour Sb. Math.
\yr 2010
\vol 201
\issue 12
\pages 1731--1775
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Linking options:
  • https://www.mathnet.ru/eng/sm7583
  • https://doi.org/10.1070/SM2010v201n12ABEH004129
  • https://www.mathnet.ru/eng/sm/v201/i12/p21
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:481
    Russian version PDF:181
    English version PDF:5
    References:46
    First page:15
     
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