Modulation instability of ion-acoustic waves (IAWs) is investigated in a collisionless unmagnetized one dimensional plasma, containing positive ions and electrons following the mixed nonextensive nonthermal distribution [Tribeche et al., Phys. Rev. E 85, 037401 (2012)]. Using the reductive perturbation technique, a nonlinear Schrödinger equation which governs the modulation instability of the IAWs is obtained. Valid range of plasma parameters has been fixed and their effects on the modulational instability discussed in detail. We find that the plasma supports both bright and dark solutions. The valid domain for the wave number k where instabilities set in varies with both nonextensive parameter q as well as non thermal parameter α. Moreover, the analysis is extended for the rational solutions of IAWs in the instability regime. Present study is useful for the understanding of IAWs in the region where such mixed distribution may exist.
The polarization force-induced changes in the dust-acoustic waves (DAWs) modulational instability (MI) are examined. Using the reductive perturbation method, the nonlinear Schrödinger equation that governs the MI of the DAWs is obtained. It is found that the effect of the polarization term R is to narrow the wave number domain for the onset of instability. The amplitude of the wave envelope decreases as R increases, meaning that the polarization force effects render weaker the associated DA rogue waves. The latter may therefore completely damp in the vicinity of R ∼ 1, i.e., as the polarization force becomes close to the electrostatic one (the net force acting on the dust particles becomes vanishingly small). The DA rogue wave profile is very sensitive to any change in the restoring force acting on the dust particles. It turns out that the polarization effects may completely smear out the DA rogue waves.
Weak ion acoustic (IA) solitary waves are investigated in a mixed nonextensive high energy-tail electron distribution, focusing on the influence of an interplay between nonthermality and nonextensivity on the IA soliton nature, its carried energy and associated rogue waves. The IA soliton exhibits compression or rarefaction depending on the strength of nonextensivity and the amount of nonthermality. The latter favors the development of rarefactive solitary structures, i.e., their corresponding q-interval enlarges as α increases. In a pure nonextensive plasma (α = 0), the energy carried by the IA soliton first decreases with q before increasing beyond a local minimum. The latter is shifted toward higher values of the nonextensive parameter q as α is increased. Moreover, nonthermal effects may render stronger the associated IA rogue waves.
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