Rotating spiral waves in a nonlinear optical system with spatial interactions

The formation of multi-petals and multi-spirals is analysed with the help of a generalized dispersion relation, taking advantage of the invariance of the rotation frequency of a pattern. It results in an eigenvalue problem, which allows us to predict the rotation frequency and the radial curvature of the pattern, in good agreement with exact calculations: 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.