Effects of superthermal electron on the features of nonlinear acoustic waves in unmagnetized collisionless ion pair plasma with superthermal electrons have been examined. The system equations are reduced in the form of the nonlinear Schrodinger equation. The rogue wave characteristics dependences on the ionic density ratio (ν = n–0/n+0), ionic mass ratio (Q = m+/m−), and superthermality index (κ) are investigated. It is worth mentioning that the results present in this work could be applicable in the Earth's ionosphere plasmas.

Modulation instability of ion-acoustic waves is investigated in a plasma composed of positive and negative ions as well as nonthermal electrons. For this purpose, a linear dispersion relation and a nonlinear Schrödinger equation are derived. The latter admits localized envelope solitary wave solutions of bright-(pulses) and dark-(holes, voids) type. The envelope soliton depends on the intrinsic plasma parameters. It is found that modulation instability of ion-acoustic waves is significantly affected by the presence of nonthermal electrons. 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-region and F-region of the Earth’s ionosphere. The findings of this investigation should be useful in understanding the stable electrostatic wave packet acceleration mechanisms in positive-negative ion plasmas, and also enhance our knowledge on the occurrence of instability associated to the propagation of the envelope ion-acoustic solitary waves in space and in laboratory plasmas where two distinct groups of ions and non-Boltzmann distributed electrons are present.

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The properties of nonlinear dust-acoustic rogue waves in an unmagnetized, collisionless, four-component dusty plasma system consisting of electrons, nonthermal ions, hot and cold dust species have been investigated. The basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of the rogue wave properties on the ion energetic population parameter is discussed. The results of the present investigation could be applicable in Saturn F-ring.

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Very recently, Wang et al (2008 Phys. Lett. A 327 417–23) proposed a method, namely the (G′/G)-expansion method, for constructing multiple travelling wave solutions of nonlinear evolution equations arising in mathematical physics. They believe that the (G′/G)-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we show that the (G′/G)-expansion method is equivalent to the extended tanh function method.

The contribution of the higher-order correction to nonlinear dust-acoustic waves are studied using the reductive perturbation method in an unmagnetized collisionless mesospheric dusty plasma. A Korteweg - de Vries (KdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation, and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution is achived via renormalization method

Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains have been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Korteweg-de Vries (KdV) equation. The effect of cold (hot) dusty plasma density n c (n h) and the charge numbers for negatively charged cold (hot) dust Z c (Z h) on the nature of DAWs are discussed.