Nonlinear Dynamics in Semiconductor Lasers 2023 - Abstract
Taki, Majid
In this work, we report the existence of drift instabilities in localised Faraday patterns induced at the surface of a fluid under a nonuniform parametric drive. The counterintuitive effect of inducing a propagating phase in the system, even when the vertical vibration modulation is fixed in space, is an intriguing attribute and differs from other experimental realisations featuring special types of boundary conditions, such as annular channels. We show that such drift is entirely induced by the nonuniform nature of the vertical drive at the bottom of the fluid container and thus cannot be observed under uniform driving. We use the normal form theory to explain the observed drift through an amplitude equation for Faraday patterns under localized driving. We demonstrate that the evolution of the instabilities at the first order of nonlinearity is described by a quintic Complex Ginzburg-Landau equation with Weber-like and self-phase modulation terms in the form of nonlinear gradients. Such nonlinear gradients trigger drift instabilities through a spontaneous nonlinear symmetry breaking above a secondary bifurcation threshold. Such nonlinear gradients trigger drift instabilities through a spontaneous nonlinear symmetry breaking above a secondary bifurcation threshold.