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Homoclinic snaking in the discrete Swift-Hohenberg equation

Kusdiantara, R and Susanto, H (2017) 'Homoclinic snaking in the discrete Swift-Hohenberg equation.' Physical Review E, 96 (6). ISSN 1539-3755

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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.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 27 Feb 2018 09:36
Last Modified: 27 Feb 2018 09:36
URI: http://repository.essex.ac.uk/id/eprint/21547

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