Variational approximations to homoclinic snaking in continuous and discrete systems
Pattern Formation and Solitons
2015-05-28 v1 Dynamical Systems
Abstract
Localised 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 lengthscales, the width of the pinning region is exponentially small and beyond the reach of standard asymptotic methods. We show how this behaviour 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. Secondly, the method is applied to a discrete system with cubic-quintic nonlinearity, giving results that agree well with numerical simulations.
Cite
@article{arxiv.1105.5268,
title = {Variational approximations to homoclinic snaking in continuous and discrete systems},
author = {P. C. Matthews and H. Susanto},
journal= {arXiv preprint arXiv:1105.5268},
year = {2015}
}
Comments
submitted. Comments are welcome