To snake or not to snake in the planar Swift-Hohenberg equation
Lloyd, D, Avitabile, D, Burke, J, Knobloch, E and Sandstede, B (2010) To snake or not to snake in the planar Swift-Hohenberg equation SIAM J. Appl. Dyn. Syst., 9 (3). 704 - 733. ISSN 1536-0040
Available under License : See the attached licence file.
Official URL: http://dx.doi.org/10.1137/100782747
We investigate the bifurcation structure of stationary localized patterns of the two dimensional Swift–Hohenberg equation on an infinitely long cylinder and on the plane. On cylinders, we find localized roll, square, and stripe patches that exhibit snaking and nonsnaking behavior on the same bifurcation branch. Some of these patterns snake between four saddle-node limits; in this case, recent analytical results predict the existence of a rich bifurcation structure to asymmetric solutions, and we trace out these branches and the PDE spectra along these branches. On the plane, we study the bifurcation structure of fully localized roll structures, which are often referred to as worms. In all the above cases, we use geometric ideas and spatial-dynamics techniques to explain the phenomena that we encounter.
|Additional Information:||Copyright 2010 Society for Industrial and Applied Mathematics|
|Divisions:||Faculty of Engineering and Physical Sciences > Mathematics|
|Deposited By:||Symplectic Elements|
|Deposited On:||19 Mar 2012 11:53|
|Last Modified:||08 Jun 2013 15:20|
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