Variational approximations to homoclinic snaking

H. Susanto, P. C. Matthews

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We investigate the snaking of localized patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, which are not accessible via standard multiple-scales asymptotic techniques. We obtain the symmetric snaking solutions and the asymmetric "ladder" states, and also predict the stability of the localized states. The resulting approximate formulas for the width of the snaking region show good agreement with numerical results.

Original languageBritish English
Article number035201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number3
DOIs
StatePublished - 31 Mar 2011

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