Homoclinic snaking in the discrete Swift-Hohenberg equation

R. Kusdiantara, H. Susanto

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8 Scopus citations

Abstract

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

Original languageBritish English
Article number062214
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume96
Issue number6
DOIs
StatePublished - 21 Dec 2017

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