Oscillating Turing Rolls as Periodic Orbits of the Lugiato-Lefever Equation

The Lugiato-Lefever equation (LLE) is a fundamental nonlinear model of pattern formation in damped-driven optical Kerr cavities with applications ranging from fiber to chip-integrated optical resonators. In standard dimensionless form the LLE describes dynamics of the intracavity field Ψ(θ,τ) as follows.