In the present investigation the modulational instability (MI) of dust acoustic wave (DAW) in four-component dusty plasma consisting of negative and positive charged dust grains and kappa (κ) distributed electrons and ions is studied. Considering the multifluid plasma model and using the reductive perturbation technique, nonlinear Schrödinger equation, which governs the MI of DAW, is obtained. It is found that presence of positive dust component, kappa-distributed electrons (κe), ions (κi), and temperature ratio (σ) significantly modify the domain of the MI and localized envelope excitations. Further, the effects of these parameters on the growth rate of MI have also been discussed in detail.

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Theoretical studies of the nonlinear self-modulation of ion acoustic waves (IAWs) in an electron–positron–ion plasma with superthermal electrons are carried out. By using the standard reductive perturbation method (RPM), the nonlinear Schrödinger equation (NLSE) is derived. The stability analysis, based on a nonlinear Schrödinger-type equation, exhibits a wide instability region, which depends on spectral index (κ), ratio of positron to electron density (p) and electron to positron temperature ratio (σ). It is found that these parameters modify the nature of modulational instability (MI) for IAWs and associated envelope solitary structures. Further, the effect of these parameters on the growth rate of MI is discussed.

As is well known, the envelope electron-acoustic (EA) nonlinear waves in one dimension are governed by the nonlinear Schrödinger equation. If transverse perturbations are considered, then this type of nonlinear wave can be described by the general form of the Davey–Stewartson equation. In this work, modulational properties of EA wave and its stability regions in two-dimensional plasma have been studied.

The higher order solutions of dust acoustic wave in dusty plasma consisting of positively charged warm adiabatic dust, negatively charged cold dust, and nonisothermally distributed electrons are studied. The Schamel-KdV equation is derived using reductive perturbation method (RPM). RPM is further extended to include the contributions of higher order terms and a generalized KdV equation is derived to observe the deviation from isothermality. Effects of nonisothermal parameter, mass and charge ratio, ratio of ion to electron temperatures, and ratio of dust to ion temperatures have been thoroughly studied. By using the renormalization method of Kodama and Taniuti [J. Phys. Soc. Jpn. 45, 298 (1978)], authors have also discussed characteristics of the dressed solitons.

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