Dust-acoustic rogue waves in a nonextensive plasma

Abstract

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.

Modulation of ion-acoustic waves in a nonextensive plasma with two-temperature electrons

“…36, 44-46, 49. We, however, mention that the physical mechanism behind the formation of rogue waves is still unclear, however, observations indicate that they have unusually steep, solitary or tightly grouped profiles, which appear like "walls of water" [41]. A large number of theoretical and experimental investigations have been reported for the study of rogue waves in various plasma systems [45,[50][51][52][53][54][55][56][57][58][59][60]. Abdelsalam [58] studied the nonlinear propagation of solitary and freak waves in a superthermal plasma with positive and negative ions, ion beam and stationary dust particles.…”

Nonlinear ion-acoustic structures in a nonextensive electron–positron–ion–dust plasma: Modulational instability and rogue waves

“…However, a number of space observations indicates the presence of particles which depart from the Maxwellian distribution. For example, the nonthermal and superthermal electrons have been observed in the Earth's bow-shock, in the upper ionosphere of Mars and in the vicinity of the Moon [14][15][16][17]. Also the non-Maxwellian electron velocity distributions have been observed and measured in the laboratory experiments [18].…”

The Modulation of a Dust Ion-Acoustic Wave in a Collisional Dusty Plasma

“…(18), is localized both in position ζ and time χ, which are equivalent respectively to the position and time variables ξ and τ . The resulting solution of the above equation then can be written as [32]: The above solution Eq. (19) predicts that the DIA wave is confined in a small region due to the nonlinear properties of the collisional dusty plasma.…”

“…(19) predicts that the DIA wave is confined in a small region due to the nonlinear properties of the collisional dusty plasma. This solution is able to concentrate a significant amount of the wave energy into a relatively small area in space [32]. In the next section, the dissipative solution, Eq.…”