Variational approximations to homoclinic snaking

Details Variational approximations to homoclinic snaking Variational approximations to homoclinic snaking

2010-09-29

arxiv.org/abs/1009.5920v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 3 figures, submitted

Scientific paper

We investigate the snaking of localised patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, that 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 localised states. The resulting approximate formulas for the width of the snaking region show good agreement with numerical results.

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