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 Schr\"odinger equation. The critical wave-number threshold kc, which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of kc against the nonextensive parameter q are found. For small kc, it is found that increasing q would lead to an increase of kc until q approaches a certain value qc, then further increase of q beyond qc decreases the value of kc. For large kc, the critical wave-number threshold kc 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 $\left({\text{H}}^{+},{\text{O}}_2^{-}\right)$ and $\left({\text{H}}^{+},{\text{H}}^{-}\right)$ 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.

Theoretical and numerical studies are performed for the nonlinear structures (explosive, solitons, and shock) in quantum electron-positron-ion magnetoplasmas. For this purpose, the reductive perturbation method is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining extended quantum Zakharov–Kuznetsov equation. The latter has been solved using the generalized expansion method to obtain a set of analytical solutions, which reflects the possibility of the propagation of various nonlinear structures. The relevance of the present investigation to the white dwarfs is highlighted.

The effect of nonthermal ions and variable dust charge on small-amplitude nonlinear dust-acoustic (DA) waves is investigated. It is found that both compressive and rarefactive solitons exist and depend on the nonthermal parameter a. Using a reductive perturbation theory, a Zakharov–Kuznetsov (ZK) equation is derived. At critical value of a, ac, a modified ZK equation with third- and fourth-order nonlinearities, is obtained. Depending on a, the solution of the evolution equation reveals whether there is coexistence of both compressive and rarefactive solitary waves or double layers (DLs) with the possibility of their two kinds. In addition, for certain plasma parameters, the solitary wave disappears and a DL is expected. The variation of dust charge number, wave velocity, and soliton amplitude and its width against system parameters is investigated for the DA solitary waves. It is shown that the incorporation of both the adiabatic dust-charge variation and the nonthermal distributed ions modifies significantly the nature of DA solitary waves and DA DLs. The findings of this investigation may be useful in understanding the ion acceleration mechanisms close to the Moon and also enhances our knowledge on pickup ions around unmagnetized bodies, such as comets, Mars, and Venus.