Dissipative Structures of the Kuramoto–Sivashinsky Equation

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 propose...

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Main Authors: N. A. Kudryashov, P. N. Ryabov, B. A. Petrov
Format: Article
Language:English
Published: Yaroslavl State University 2015-02-01
Series:Моделирование и анализ информационных систем
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Online Access:https://www.mais-journal.ru/jour/article/view/234
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author N. A. Kudryashov
P. N. Ryabov
B. A. Petrov
author_facet N. A. Kudryashov
P. N. Ryabov
B. A. Petrov
author_sort N. A. Kudryashov
collection DOAJ
description 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.
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publishDate 2015-02-01
publisher Yaroslavl State University
record_format Article
series Моделирование и анализ информационных систем
spelling doaj-art-021f2a0e47ce462e98a3625f5245f03a2025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-02-0122110511310.18255/1818-1015-2015-1-105-113227Dissipative Structures of the Kuramoto–Sivashinsky EquationN. A. Kudryashov0P. N. Ryabov1B. A. Petrov2National Research Nuclear University MEPhINational Research Nuclear University MEPhINational Research Nuclear University MEPhIIn 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.https://www.mais-journal.ru/jour/article/view/234kuramoto–sivashinsky equationself–organizationpatternspseudospectral methodnumerical simulation
spellingShingle N. A. Kudryashov
P. N. Ryabov
B. A. Petrov
Dissipative Structures of the Kuramoto–Sivashinsky Equation
Моделирование и анализ информационных систем
kuramoto–sivashinsky equation
self–organization
patterns
pseudospectral method
numerical simulation
title Dissipative Structures of the Kuramoto–Sivashinsky Equation
title_full Dissipative Structures of the Kuramoto–Sivashinsky Equation
title_fullStr Dissipative Structures of the Kuramoto–Sivashinsky Equation
title_full_unstemmed Dissipative Structures of the Kuramoto–Sivashinsky Equation
title_short Dissipative Structures of the Kuramoto–Sivashinsky Equation
title_sort dissipative structures of the kuramoto sivashinsky equation
topic kuramoto–sivashinsky equation
self–organization
patterns
pseudospectral method
numerical simulation
url https://www.mais-journal.ru/jour/article/view/234
work_keys_str_mv AT nakudryashov dissipativestructuresofthekuramotosivashinskyequation
AT pnryabov dissipativestructuresofthekuramotosivashinskyequation
AT bapetrov dissipativestructuresofthekuramotosivashinskyequation