Kozyreff, G. and Chapman, S. J. (2006) Asymptotics of large bound states of localized structures. Physical Review Letters, 97 (4). 044502. ISSN 00319007
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Official URL: http://link.aps.org/abstract/PRL/v97/e044502
Abstract
We analyze stationary fronts connecting uniform and periodic states emerging from a patternforming 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 multiplescale expansion. We apply the method to the SwiftHohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling.
Item Type:  Article 

Subjects:  O  Z > Partial differential equations O  Z > Ordinary differential equations 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  297 
Deposited By:  Jon Chapman 
Deposited On:  04 Oct 2006 
Last Modified:  29 May 2015 18:19 
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