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We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schrödinger equation. The critical wave-number threshold k(c), which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k(c) against the nonextensive parameter q are found. For small k(c), it is found that increasing q would lead to an increase of k(c) until q approaches a certain value q(c), then further increase of q beyond q(c) decreases the value of k(c). For large k(c), the critical wave-number threshold k(c) is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.

Properties of fully nonlinear ion-acoustic solitary waves in a plasma with positive-negative ions and nonthermal electrons are investigated. For this purpose, the hydrodynamic equations for the positive-negative ions, nonthermal electron density distribution, and the Poisson equation are used to derive the energy integral equation with a new Sagdeev potential. The latter is analyzed to examine the existence regions of the solitary pulses. It is found that the solitary excitations strongly depend on the mass and density ratios of the positive and negative ions as well as the nonthermal electron parameter. Numerical solution of the energy integral equation clears that both positive and negative potentials exist together. It is found that faster solitary pulses are taller and narrower. Furthermore, increasing the electron nonthermality parameter (negative-to-positive ions density ratio) decreases (increases) the localized excitation amplitude but increases (decreases) the pulse width. The present model is used to investigate the solitary excitations in the (H+,O2−) and (H+,H−) plasmas, where they are presented in the D- and F-regions of the Earth's ionosphere. This investigation should be helpful in understanding the salient features of the fully nonlinear ion-acoustic solitary waves in space and in laboratory plasmas where two distinct groups of ions and non-Boltzmann distributed electrons are present