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The emergence of a coherent structure for coherent structures: localized states in nonlinear systems


Reference:

Dawes, J. H. P., 2010. The emergence of a coherent structure for coherent structures: localized states in nonlinear systems. Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, 368 (1924), pp. 3519-3534.

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Official URL:

http://dx.doi.org/10.1098/rsta.2010.0057

Abstract

Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific subclass of such problems, in which a pattern-forming, or ‘Turing’, instability occurs, rapid progress has been made recently in our understanding of the formation of localized states: patches of regular pattern surrounded by the unpatterned homogeneous background state. This short review article surveys the progress that has been made for localized states and proposes three areas of application for these ideas that would take the theory in new directions and ultimately be of substantial benefit to areas of applied science. Finally, I offer speculations for future work, based on localized states, that may help researchers to understand coherent structures more generally.

Details

Item Type Articles
CreatorsDawes, J. H. P.
DOI10.1098/rsta.2010.0057
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code19824
Additional InformationOne contribution of 18 to a Triennial Issue ‘Visions of the future for the Royal Society’s 350th anniversary year’.

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