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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 4, Pages 685–693
DOI: https://doi.org/10.7868/S0044466916040177 (Mi zvmmf10377) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Nonlinear waves described by a fifth-order equation derived from the Fermi–Pasta–Ulam system

A. K. Volkov, N. A. Kudryashov

National Engineering Physics Institute "MEPhI", Moscow
Full-text PDF (424 kB) Citations (4)
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DOI: https://doi.org/10.7868/S0044466916040177
Abstract: Nonlinear wave processes described by a fifth-order generalized KdV equation derived from the Fermi–Pasta–Ulam (FPU) model are considered. It is shown that, in contrast to the KdV equation, which demonstrates the recurrence of initial states and explains the FPU paradox, the fifthorder equation fails to pass the Painlevé test, is not integrable, and does not exhibit the recurrence of the initial state. The results of this paper show that the FPU paradox occurs only at an initial stage of a numerical experiment, which is explained by the existence of KdV solitons only on a bounded initial time interval.
Key words: Fermi–Pasta–Ulam problem, nonlinear differential equations, pseudospectral method, numerical simulation.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00493_а
This work was supported by the Russian Foundation for Basic Research, project no. 14-01-00493.
Received: 16.06.2015
Revised: 04.09.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 4, Pages 680–687
DOI: https://doi.org/10.1134/S0965542516040151
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. K. Volkov, N. A. Kudryashov, “Nonlinear waves described by a fifth-order equation derived from the Fermi–Pasta–Ulam system”, Zh. Vychisl. Mat. Mat. Fiz., 56:4 (2016), 685–693; Comput. Math. Math. Phys., 56:4 (2016), 680–687
Citation in format AMSBIB
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