Nonlinear instability of dust ion-acoustic waves in a plasma with strongly correlated dust grains

The nonlinear propagation of large amplitude dust ion-acoustic waves in a strongly coupled dusty plasma is considered. By employing a two-fluid model, we derive an equation for the dust ion-acoustic (DIA) waves in the presence of ion density fluctuations of dust acoustic waves. The relevant equation for the latter in the presence of the DIA ponderomotive force is obtained by means of the generalized viscoelastic hydrodynamics equations for strongly correlated dust grains, along with a Boltzmann electron distribution and a modified (by the DIA ponderomotive force) Boltzmann ion distribution. The newly derived coupled mode equations are Fourier analyzed to obtain a nonlinear dispersion relation that is useful for investigating the decay and modulational instabilities of coherent DIA waves. The implications to laboratory plasmas are pointed out.