Theoretical investigations depending on the observation data are carried out for the nonlinear amplitude modulation of ion-acoustic waves propagating in an unmagnetized plasma composed of Maxwellian electrons and light negative ions in addition to mobile cold positive ions. The basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE) for describing the modulational instability process. The regions of the stable and unstable wavepackets have been confined precisely for various regimes. Moreover, the criteria for the existence of the breathers have been obtained. Analytical solutions of the NLSE in the forms of Akhmediev breathers, Kuznetsov-Ma (KM) solitons, and rogue waves are obtained. The characteristics of the profile of Akhmediev breathers, KM solitons, and freak waves are examined depending on the relevant physical parameters of the observed data.

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The quantum hydrodynamic model is employed to investigate the effects of gravitational potential on multicomponent dusty plasmas. The effects of Fermi temperature ratios of ions to electrons (TF i/TF e) and positrons to electrons (TF p/TF e) have been calculated and presented graphically. It is observed that an increase in the Fermi temperature ratios of ions to electrons and positrons to electrons stabilizes the Jeans instability as the mode phase speed increases with these ratios. In the absence of the statistical effects due to Fermi pressure, the dispersion is weak. The stability criteria are calculated for each case separately.

Arbitrary amplitude ion-acoustic waves in an unmagnetized plasma consisting of cold positive ions, superthermal electrons, and positrons beam are reported. The basic set of fluid equations is reduced to an energy-balance like equation. The latter is numerically analyzed to examine the existence regions for solitary and shock waves. It is found that only solitary waves can propagate, however, the model cannot support shocks. The effects of superthermality and beam parameters (via, positrons concentration and streaming velocity) on the existence region, as well as solitary wave profile have been discussed.

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We employ quasipotential analysis to derive the Sagdeev potential which accounts for the effect of electron trapping in a warm electronegative plasma with κ-distributed electrons. The trapped electron density is truncated to some finite order of the electrostatic potential Φ. This consequently leads to an extended KdV equation which gives rise to small amplitude double layers (SIADLs). The effects of various plasma parameters, e.g., superthermality index, the electron trapping efficiency, the mass ratio of negative to positive ion, the number density ratio of electron to positive ion, and temperature ratio of positive ion to electron on the small amplitude ion acoustic double layers (SIADLs), have been investigated. It has been found that these parameters have a significant modifying role in the SIADLs.