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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 192, Number 1, Pages 41–50
DOI: https://doi.org/10.4213/tmf9263 (Mi tmf9263) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Families of exact solutions for linear and nonlinear wave equations with a variable speed of sound and their use in solving initial boundary value problems

E. V. Trifonovab

a Institute of Automation and Control Processes, Far Eastern Branch, RAS, Vladivostok, Russia
b Far Eastern Federal University, Vladivostok, Russia
Full-text PDF (375 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf9263
Abstract: We propose a procedure for multiplying solutions of linear and nonlinear one-dimensional wave equations, where the speed of sound can be an arbitrary function of one variable. We obtain exact solutions. We show that the functional series comprising these solutions can be used to solve initial boundary value problems. For this, we introduce a special scalar product.
Keywords: exact solution, wave equation, Bäcklund transformation.
Received: 21.07.2016
Revised: 16.11.2016
English version:
Theoretical and Mathematical Physics, 2017, Volume 192, Issue 1, Pages 974–981
DOI: https://doi.org/10.1134/S0040577917070030
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. V. Trifonov, “Families of exact solutions for linear and nonlinear wave equations with a variable speed of sound and their use in solving initial boundary value problems”, TMF, 192:1 (2017), 41–50; Theoret. and Math. Phys., 192:1 (2017), 974–981
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9263
  • https://www.mathnet.ru/eng/tmf/v192/i1/p41
    • This publication is cited in the following 3 articles:
    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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    Abstract page:388
    Full-text PDF :128
    References:62
    First page:24
     
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