Ni. Zheleznykh et al., ROTATING SPIRAL WAVES IN A NONLINEAR-OPTICAL SYSTEM WITH SPATIAL INTERACTIONS, Chaos, solitons and fractals, 4(8-9), 1994, pp. 1717-1728
The formation of multi-petals and multi-spirals is analysed with the h
elp of a generalized dispersion relation, taking advantage of the inva
riance of the rotation frequency of a pattern. It results in an eigenv
alue problem, which allows us to predict the rotation frequency and th
e radial curvature of the pattern, in good agreement with exact calcul
ations: A stationary pattern is predicted to look like petals, while a
uniform rotating pattern is predicted to have some curvature, leading
to a spiral shape.