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Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

Zelik, S and Mielke, A (2009) Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 198 (925). VI-95.

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Abstract

We study semilinear parabolic systems on the full space Rn that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. We prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, we verify the existence of SinaiBunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Zelik, SUNSPECIFIEDUNSPECIFIED
Mielke, AUNSPECIFIEDUNSPECIFIED
Date : 1 March 2009
Copyright Disclaimer : Copyright 2009 by the American Mathematical Society. All rights reserved.
Uncontrolled Keywords : Science & Technology, Physical Sciences, Mathematics, dissipative systems, unbounded domains, multi-pulses, normal hyperbolicity, center-manifold reduction, space-time chaos, Bernoulli shifts, REACTION-DIFFUSION SYSTEMS, ORDINARY DIFFERENTIAL-EQUATIONS, SINGULAR PERTURBATION PROBLEMS, SWIFT-HOHENBERG EQUATION, LOCALIZED STRUCTURES, REVERSIBLE-SYSTEMS, UNBOUNDED-DOMAINS, CENTER MANIFOLDS, MAP LATTICES, INSTABILITY
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 03 Nov 2016 13:40
Last Modified : 03 Nov 2016 13:40
URI: http://epubs.surrey.ac.uk/id/eprint/812222

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