Pattern control and suppression of spatiotemporal chaos using geometrical resonance

We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger, 4, and Complex Ginzburg–Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743].