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Asymptotics of large bound states of localized structures

Abstract:

We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifur...

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Publication date:
2006-07-28
URN:
uuid:55f3b061-f20e-4497-8b9b-93aeab02e108
Local pid:
oai:eprints.maths.ox.ac.uk:297

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