Paper Info
Title
Dissipative structures of the Kuramoto-Sivashinsky equation.
Abstract
The features of dissipative structure formation, which is described by the periodic boundary value problem for the Kuramoto–Sivashinsky equation, are investigated. A numerical algorithm based on the pseudospectral method is presented. The efficiency and accuracy of the proposed numerical method are proved using the exact solution of the equation under study. Using the proposed method, the process of dissipative structure formation, which is described by the Kuramoto–Sivashinsky equation, is studied. The quantitative and qualitative characteristics of this process are described. It is shown that there is a value of the control parameter for which the dissipative structure formation processes occur. Via cyclic convolution, the average value of the control parameter is found. In addition, the dependence of the amplitude of the formed structures on the value of the control parameter is analyzed.
Year
DOI
Venue
2015
10.3103/S0146411615070147
Automatic Control and Computer Sciences
Keywords
Field
DocType
Kuramoto–Sivashinsky equation, self-organization, patterns, pseudospectral method, numerical simulation
Exact solutions in general relativity,Boundary value problem,Mathematical optimization,Mathematical analysis,Dissipative system,Circular convolution,Numerical analysis,Periodic graph (geometry),Amplitude,Mathematics,Pseudo-spectral method
Journal
Volume
Issue
ISSN
49
7
1558-108X
Citations 
PageRank 
References 
0
0.34
2
Authors
3
Name
Order
Citations
PageRank
Nikolai A. Kudryashov19719.20
Pavel N. Ryabov2326.19
B. A. Petrov300.34