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A rigorous theoretical investigation has been performed on dust-acoustic (DA) solitary structures in an unmagnetized dusty plasma, consisting of negatively charged mobile dust grains, Boltzmann distributed electrons, and nonthermally distributed ions of two distinct temperatures. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV) and Gardner equations, and their solitary waves (SWs) and double layer (DL) (in case of Gardner equation) solutions are derived by using the reductive perturbation technique. The basic features of the DA Gardner solitons (GSs) and DLs are studied analytically as well as numerically. It has been observed that the GSs significantly differ from K-dV and mK-dV solitons, and only positive potential DLs exist in the system. It is also studied that two-temperature nonthermal ions significantly modify the nature and basic properties of the DA SWs. The present investigation can be very effective for understanding and studying the nonlinear characteristics of the DA waves in laboratory and space dusty plasmas.

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A rigorous theoretical investigation has been made on dust-acoustic (DA) shock structures in an unmagnetized dusty plasma system whose constituents are negatively charged cold mobile dust fluid, electrons following Boltzmann distribution, and positively charged ions of two distinct temperatures following nonextensive (q) and nonthermal distributions, respectively. In this paper, the Burgers' equation has been derived by employing reductive perturbation technique which is valid for small but finite amplitude limit. It is observed that both the nonextensive and nonthermal ions of two distinct temperatures and dust kinematic viscosity significantly modify the basic properties (amplitudes, width, and polarities) of the DA shockwaves (DASHWs). The effects of low (high) temperature ions following nonextensive (nonthermal) and dust kinematic viscosity on DASHWs are examined both analytically and numerically. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned. IndexTerms-Dust-acoustic shockwaves (DASHWs), nonthermal ions, two-temperature ions.