Variational approximations to homoclinic snaking in continuous and discrete systems

P. C. Matthews, H. Susanto

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Localized structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separation of length scales, the width of the pinning region is exponentially small and beyond the reach of standard asymptotic methods. We show how this behavior can be obtained using a variational method, for two systems. In the case of the quadratic-cubic Swift-Hohenberg equation, this gives results that are in agreement with recent work using exponential asymptotics. In addition, the method is applied to a discrete system with cubic-quintic nonlinearity, giving results that agree well with numerical simulations.

Original languageBritish English
Article number066207
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - 19 Dec 2011


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