The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for q<qc (q>qc) (where qc is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.

The nonlinear propagation of dust-acoustic (DA) waves in an obliquely propagating magnetized dusty plasma, containing nonextensively distributed electrons of distinct temperatures (namely lower and higher temperature nonextensive electrons), negatively charged mobile dust grains, and Maxwellian ions, is rigorously studied and analyzed by deriving the Zakharov-Kuznetsov equation. It is found that the characteristics of the DA solitary waves (DASWs) are significantly modified by the external magnetic field, obliqueness of the system, nonextensivity of the electrons, electron temperature-ratios, and the respective number densities of two species of electrons. The results obtained from this analysis can be employed in understanding and treating the structures and the characteristics of DASWs both in laboratory and astrophysical plasma system.

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The propagation of dust-acoustic shock waves (DASWs) in a collisionless unmagnetized dusty plasma (containing super-thermal electrons of two distinct temperatures, non-thermal ions, and a negatively charged viscous dust fluid) has been theoretically investigated by deriving and solving the nonlinear Burgers' equation. It has been observed that the viscous force acting on the dust fluid is a source of dissipation, and is responsible for the formation of DASWs, and that the basic features (viz., amplitude, polarity, width, etc.) of the DASWs are significantly modified by the presence of super-thermal electrons and non-thermal ions. The possible applications of this investigation in Earth's mesosphere, the solar atmosphere, Saturn's magnetosphere, etc., have also been briefly addressed.