Steady solutions of the Kuramoto-Sivashinsky equation
type: Item
instance of: scholarly article
title: Steady solutions of the Kuramoto-Sivashinsky equation
zbMATH Open document ID: 0603.35080
DOI: 10.1016/0167-2789(86)90055-2
author: Daniel Michelson
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: Steady solutions of the Kuramoto-Sivashinsky equation are studied. These solutions are defined on the whole x line and propagate with a constant speed \(c^ 2\) in time. For large \(c^ 2\) it is shown that the solution is unique and has a conical form. For small \(c^ 2\) there is a periodic solution and an infinite set of quasi-periodic solutions as asserted by Moser's twist map theorem. Numerical computations for intermediate values of \(c^ 2\) suggests that below \(c^ 2\approx 1.6\) for every speed there is a continuum of odd quasi-periodic solutions or a Cantor set of chaotic solutions wrapped by infinite sequences of conic solutions.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B15
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 3973463
zbMATH Keywords: reaction diffusion
zbMATH Keywords: flame front propagation
zbMATH Keywords: Steady solutions
zbMATH Keywords: Kuramoto- Sivashinsky equation
zbMATH Keywords: unique
zbMATH Keywords: periodic solution
zbMATH Keywords: quasi-periodic solutions
zbMATH Keywords: twist map theorem
zbMATH Keywords: Numerical computations
zbMATH Keywords: chaotic solutions
zbMATH Keywords: conic solutions
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90055-2
OpenAlex ID: W2067139588
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description: scientific article; zbMATH DE number 3973463