Snaking of radial solutions of the multi-dimensional Swift–Hohenberg equation: A numerical study

The bifurcation structure of localized stationary radial patterns of the Swift–Hohenberg equation is explored when a continuous parameter nn is varied that corresponds to the underlying space dimension whenever nn is an integer. In particular, we investigate how 1D pulses and 2-pulses are connected to planar spots and rings when nn is increased from 1 to 2. We also elucidate changes in the snaking diagrams of spots when the dimension is switched from 2 to 3.