Synchronization of Nonlinear Waves in Dusty Plasma

Synchronization is a collective nonlinear phenomenon in which two or more systems develop rhythmic synchrony for certain characteristic frequencies through weak nonlinear interactions1. It is observed in the collection of discrete systems or in a fluid or fluid-like continuum medium1. We present a theoretical model of the synchronization of natural acoustic modes in dusty plasma treated as a charged fluid. The one-dimensional model is based on a forced Korteweg-de Vries-Burgers (fKdV-B) formulation of the dust fluid dynamics in the weak nonlinearity reqime2. Synchronization of dust density or dust acoustic waves, driven by an external frequency source, has been explored in various dusty plasma experiments 3-5. However, there is no available theoretical model based on a wave equation exhibiting both nonlinearity and dispersion in a plasma that can successfully describe the global synchronization of propagating waves
^3-5
. We have demonstrated that the fKdV-B model shows harmonic (1:1) and super-harmonic (1:2) synchronization states using a cnoidal square driver of traveling waveform2. The domains of synchronized states are delineated in the Arnold tongue, showing excellent quantitative agreement with dusty plasma experiment3. The fKdV-B model can explain the synchronization of waves in nonlinear dispersive systems with fluid-like convective nonlinearity.