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Coherent structures emerge from the dynamics of many kinds of dissipative,externally driven, nonlinear systems, and continue to provoke new questionsthat challenge our physical and mathematical understanding. In one specificsub-class of such problems, where a pattern-forming, or `Turing', instabilityoccurs, rapid progress has been made recently in our understanding of theformation of localized states: patches of regular pattern surrounded by theunpatterned homogeneous background state. This short review article surveys theprogress that has been made for localized states, proposes three areas ofapplication for these ideas that would take the theory in new directions andultimately be of substantial benefit to areas of applied science. Finally Ioffer speculations for future work, based on localized states, that may helpresearchers to understand coherent structures more generally.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

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