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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 2, Pages 253–266
DOI: https://doi.org/10.7868/S0044466915020076 (Mi zvmmf10155) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Stability of nonstationary solutions of the generalized KdV-Burgers equation

A. P. Chugainovaa, V. A. Shargatovb

a Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
b National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe sh. 31, Moscow, 115409, Russia
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DOI: https://doi.org/10.7868/S0044466915020076
Abstract: The stability of nonstationary solutions to the Cauchy problem for a model equation with a complex nonlinearity, dispersion, and dissipation is analyzed. The equation describes the propagation of nonlinear longitudinal waves in rods. Previously, complex behavior of traveling waves was found, which can be treated as discontinuity structures in solutions of the same equation without dissipation and dispersion. As a result, the solutions of standard self-similar problems constructed as a sequence of Riemann waves and shocks with a stationary structure become multivalued. The multivaluedness of the solutions is attributed to special discontinuities caused by the large effect of dispersion in conjunction with viscosity. The stability of special discontinuities in the case of varying dispersion and dissipation parameters is analyzed numerically. The computations performed concern the stability analysis of a special discontinuity propagating through a layer with varying dispersion and dissipation parameters.
Key words: generalized KdV-Burgers equation, stability of nonstationary solutions, difference solution method.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12047
Received: 16.07.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 2, Pages 251–263
DOI: https://doi.org/10.1134/S0965542515020074
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. P. Chugainova, V. A. Shargatov, “Stability of nonstationary solutions of the generalized KdV-Burgers equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:2 (2015), 253–266; Comput. Math. Math. Phys., 55:2 (2015), 251–263
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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