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The propagation of ion acoustic waves (IAWs) in plasmas composed of ions and nonextensive electrons and positrons is investigated. By means of the reduction perturbation technique, a nonlinear Schrödinger equation is derived and the modulation instability (MI) of ion acoustic waves is analyzed in detail. The effects of different ranges of the nonextensive parameter q on the MI are studied. The growth rate of the MI is also given for different values of the q parameter. It is also found that the ratio of the electron temperature to positron temperature and the ratio of the positron density to electron density modify the nature of IAWs instability and the solitary structures.

Weak ion-acoustic double-layers (IA-DLs) in a two-component plasma are investigated in the context of the nonextensive statistics proposed by Tsallis. Due to the entropic index q, our plasma model can admit compressive as well as rarefactive IA-DLs. It is shown that the values 5 3 < q < 3 are automatically ruled out from the domain of allowable nonextensive q-parameters for the existence of smallDLs. As long as the Mach number M is less than ∼1.42, the only admissible q-values which may lead to IA-DLs are all positive. For −1 < q < 1 (1 < q < 5/3), the effect of increasing q is to lower (to shift towards higher values) the critical Mach number M cr above which only compressive IA-DL are admitted. Beyond q = 3, only compressive smallamplitude ion-acoustic double layers are observed. Furthermore, due to the flexibility of the q-parameter, the obtained results bring a possibility to deal with small-DLs with relatively high Mach numbers. Our investigation may be of wide relevance to astronomers and space scientists working on interstellar plasmas.

The head-on collision between two electronacoustic solitary waves (EASWs) in an unmagnetized plasma is investigated, including a cold electrons fluid, hot electrons, obeying a nonextensive distribution and stationary ions. By using the extended Poincaré-Lighthill-Kuo (PLK) perturbation method, the analytical phase shifts following the head-on collision are derived. The effects of the ratio of the number density of hot electrons to the number density of cold electrons α, and the nonextensive parameter q on the phase shifts are studied. It is found that q and the hot-to-cold electron density ratio significantly modify the phase shifts.

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Ion acoustic shock waves (IASWs) are studied in a plasma consisting of electrons, positrons and ions. Boltzmann distributed positrons and superthermal electrons are considered in the plasma. The dissipation is taken into account the kinematic viscosity among the plasma constituents. The Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived by reductive perturbation method. Shock waves are solutions of KdV-Burgers equation. It is observed that an increasing positron concentration decreases the amplitude of the waves. Furthermore, in the existence of the kinematic viscosity among the plasma, the shock wave structure appears. The effects of ion kinematic viscosity (η 0 ) and the superthermal parameter (k) on the ion acoustic waves are found.

Electron-acoustic double-layers (EA-DLs) are addressed in a plasma with a q-nonextensive electron velocity distribution. The domain of their allowable Mach numbers depends drastically on the plasma parameters and, in particular, on the electron nonextensivity. As the electrons evolve far away from their thermodynamic equilibrium, the negative EA-DLs shrinks and may develop into compressive EA-DLs. Our results may be relevant to the double-layers observed both in the auroral region and the plasma sheet of Earth's magnetosphere (during enhanced magnetic activity). These DLs associated parallel electric fields are thought to be responsible for particle (electrons and ions) acceleration. Furthermore, our theoretical analysis brings a possibility to develop more refined theories of nonlinear cosmic DLs that may occur in astrophysical plasmas.

In this paper, the characteristics of the head-on collision of ion-acoustic solitary waves (IASWs) in the collisionless magnetic-field-free plasma consisting of cold ions, nonextensive electrons and thermal positrons are discussed using the extended Poincaré-Lighthill-Kuo method. Two Kortewege-de Vries equations for solitary waves are derived and the analytical phase shifts after the head-on collision of two solitary waves are also obtained. The effects of the electron nonextensive distribution (q-parameter) on the phase shifts of both the colliding solitary waves are studied. It is found that the presence of nonextensive electrons plays a significant role in the collision of IASWs.