The nonlinear propagation of small amplitude dust-acoustic (DA) solitary waves in magnetized dusty plasma consisting of negatively charged mobile dust fluid, and Boltzmann-distributed electrons and ions with two distinct temperatures following a q-nonextensive distribution are investigated. In this article, a number of nonlinear equations, namely, the Korteweg–de-Vries (K-dV) equations, have been derived by employing the reductive perturbation technique that is valid for a small but finite amplitude limit. The effects of nonextensivity of ions with two distinct temperatures and dust concentration on the amplitude and width of DA solitary waves are investigated theoretically. It is observed that both the nonextensive and low-temperatures ions significantly modify the basic properties and polarities of DA solitary waves. It is shown that both positive and negative potential DA solitons occur in this case. 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.
