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Model. Anal. Inform. Sist., 2015, Volume 22, Number 1, Pages 105–113 (Mi mais423)  

Dissipative structures of the Kuramoto–Sivashinsky equation

N. A. Kudryashov, P. N. Ryabov, B. A. Petrov

National Research Nuclear University MEPhI, Kashirskoe shosse, 31, Moscow, 115409, Russia

Abstract: In the present work, we study the features of dissipative structures formation described by the periodic boundary value problem for the Kuramoto-Sivashinsky equation. The numerical algorithm which is based on the pseudospectral method is presented. We prove the efficiency and accuracy of the proposed numerical method on the exact solution of the equation considered. Using this approach, we performed the numerical simulation of dissipative structure formations described by the Kuramoto–Sivashinsky equation. The influence of the problem parameters on these processes are studied. The quantitative and qualitative characteristics of dissipative structure formations are described. We have shown that there is a value of the control parameter at which the processes of dissipative structure formation are observed. In particular, using the cyclic convolution we define the average value of this parameter. Also, we find the dependence of the amplitude of the structures on the value of control parameter.

Keywords: Kuramoto–Sivashinsky equation, self–organization, patterns, pseudospectral method, numerical simulation.

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Bibliographic databases:
UDC: 532.592
Received: 20.12.2014

Citation: N. A. Kudryashov, P. N. Ryabov, B. A. Petrov, “Dissipative structures of the Kuramoto–Sivashinsky equation”, Model. Anal. Inform. Sist., 22:1 (2015), 105–113

Citation in format AMSBIB
\Bibitem{KudRyaPet15}
\by N.~A.~Kudryashov, P.~N.~Ryabov, B.~A.~Petrov
\paper Dissipative structures of the Kuramoto--Sivashinsky equation
\jour Model. Anal. Inform. Sist.
\yr 2015
\vol 22
\issue 1
\pages 105--113
\mathnet{http://mi.mathnet.ru/mais423}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3417815}
\elib{http://elibrary.ru/item.asp?id=23237973}


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