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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 2, Pages 244–252
DOI: https://doi.org/10.7868/S0044466918020102 (Mi zvmmf10678) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Traveling-wave solutions of the Kolmogorov–Petrovskii–Piskunov equation

S. V. Pikulin

Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia
Citations (11)
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DOI: https://doi.org/10.7868/S0044466918020102
Abstract: We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov–Petrovskii–Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.
Key words: Kolmogorov–Petrovskii–Piskunov equation, generalized Fisher equation, Abel's equation of the second kind, Fuchs–Kowalewski–Painlevé test, self-similar solutions, traveling waves, intermediate asymptotic regime.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00781_а
Received: 12.07.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 2, Pages 230–237
DOI: https://doi.org/10.1134/S0965542518020124
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: S. V. Pikulin, “Traveling-wave solutions of the Kolmogorov–Petrovskii–Piskunov equation”, Zh. Vychisl. Mat. Mat. Fiz., 58:2 (2018), 244–252; Comput. Math. Math. Phys., 58:2 (2018), 230–237
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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