Dust-acoustic envelope solitons in strongly coupled dusty plasmas

The propagation nature and the modulational instability (MI) criteria of low frequency amplitude modulated dust-acoustic envelope solitons are analyzed theoretically and numerically in an unmagnetized dusty plasma consisting of strongly coupled micron-sized inertial dust grains, Boltzmann distributed non-inertial electrons and ions. A hydrodynamical fluid model approach is used, based on [V. V. Yaroshenko, F. Verheest, H. M. Thomas and G.E. Morfill, New J. Phys. 11, 073013 (2009); V. V. Yaroshenko, V. Nosenko, and G. E. Morfill, Phys. Plasmas, 17, 103709 (2010)], where the strong coupling between dust grains for by an effective electrostatic pressure is accounted, which is in fact a dynamical function of the dust-density and the electrostatic potential. It is seen that the strong coupling between dust particles due to the effective electrostatic ``pressure modifies the wavepacket stability and affects the occurrence of MI. A cubic nonlinear Schrodinger-type equation, which describes the evolution of the wavepacket's envelope, is derived by adopting a multiscale technique for the amplitude dynamics. It is shown that long-wavelength dust-acoustic wavepackets are stable, while MI sets in beyond a carrier wavenumber threshold, which is evaluated in terms of intrinsic plasma parameters of relevance. On the other hand, the MI window is larger for higher ion density. The effect of the ion number density on MI is twofold, in that a higher ion density leads to a higher threshold (thus, the wave will be modulationally unstable for the larger values of the carrier wavenumber) but it also entails a wider instability window (hence, external perturbations must be of specific wavenumbers to trigger the instability). Numerical simulation confirms that the bright-type envelope soliton solution is stable beyond the carrier wavenumber threshold, i.e., in the modulationally unstable region, while the dark type envelope soliton is stable for wavenumbers below the threshold.