Rogue Waves Generator and Chaotic and Fractal Behavior of the Maccari System with a Resonant Parametric Forcing

Abstract

Using the Asymptotic Perturbation (AP) method we can find approximate solutions for the Maccari equation with a parametric resonant forcing acting over the frequency of a generic mode. Taking into account its nonlocal behavior and applying symmetry considerations, a system with two coupled equations for the phase and amplitude modulation can be obtained. The system can be solved, and we demonstrate the existence of a big modulation in the wave amplitude, producing a rogue waves train and, in this case, these waves are not isolated. We then obtain a rogue waves generator, being able of producing and controlling the rogue waves’ amplitude. Another important finding is the existence of chaotic or fractal solutions, because of the presence of an arbitrary function in the solution.