title: Variational approximations to homoclinic snaking.
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.
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG72RD, United Kingdom.
authors.forename: H
authors.initials: H
authors.lastname: Susanto
authors.forename: P C
authors.initials: PC
authors.lastname: Matthews