Chaos and coherent structures in partial differential equations
type: Item
instance of: scholarly article
title: Chaos and coherent structures in partial differential equations
zbMATH Open document ID: 0596.58029
DOI: 10.1016/0167-2789(86)90165-X
author: Hatsuo Adachihara
author: Juan Carlos Lerman
author: J. V. Moloney
author: Alan C. Newell
author: Alejandro B. Aceves
author: Christopher K. R. T. Jones
author: David W. McLaughlin
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: The general purpose of this paper is the understanding of nonpredictable behaviour in nonlinear partial differential equations which have, in certain parameter ranges, the qualitative property of solution sensitivity with respect to initial conditions. More particularly, the authors explore the appealing idea of modern dynamics that the apparently stochastic time behaviour of large and even infinite-dimensional nonlinear systems is in fact a manifestation of a deterministic solution orbit on a low-dimensional chaotic attractor. Then a natural question concerns the possibility and the methods of identification of some physical characteristics such as the spatial structure of those few active modes dominating the dynamics. It is essentially to this problem that the paper is devoted. The authors begin with a set of governing equations and derive from it a simpler system which uniformly captures the dynamical behaviour of the former. The achievement of this plan is carried out by using fully nonlinear systems which are close to exactly integrable. The specific situation considered here is that of long term behaviour of electromagnetic waves in nonlinear passive optical cavities.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 81V80
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 3960609
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: stochasticity
zbMATH Keywords: turbulence
zbMATH Keywords: solitary waves
zbMATH Keywords: lasers
zbMATH Keywords: optical bistability
zbMATH Keywords: nonlinear partial differential equations
zbMATH Keywords: chaotic attractor
reviewed by: Christian Mira
MaRDI profile type: Publication
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full work available at URL: 0167-2789(86)90165-x
OpenAlex ID: W2048803006
description: scientific article; zbMATH DE number 3960609