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The propagation of the small amplitude ion-acoustic solitary waves (IASWs) is studied in a plasma containing cold fluid ions and multi-temperature electrons (cool and hot electrons) with the nonextensive distribution. In this paper, we were firstly written a set of fluid equations in the spherical geometry. Then, spherical Korteweg–de Vries (KdV) equation was derived using a reductive perturbation method. The obtained spherical Korteweg–de Vries equation was solved using a homotopy perturbation method (HPM). Furthermore, the impact of the electron nonextensivity, the density ratio of electrons and ions and the temperature ratio on the characteristics of ion- acoustic solitary waves were studied. The analytical results show that a decrease in the electron nonextensivity increases the soliton ion- acoustic width. On the other word, it was observed that a reduction in the nonextensivity parameter increases the nonlinear coefficient of the KdV equation.

The propagation of nonlinear quantum dust ion-acoustic (QDIA) solitary waves in a unmagnetized quantum plasma whose constituents are inertialess quantum electrons and positrons, classical cold ions and stationary negative dust grains are studied by deriving the Korteweg–de Vries (KdV) equation under the reductive perturbation method. Quantum Hydrodynamic (QHD) equations are used to take into account the quantum diffraction in quantum statistics corrections. It is shown that depending on some critical values of the dust density (d) which is function of quantum diffraction parameter (H), both rarefactive and compressive type of solitons can exist in the model plasma. Further, the amplitude and width of both solitons increase as d increases. Moreover, it is pointed out that an increase in quantum diffraction parameter, decreases the width of compressive soliton but increases the width of rarefactive soliton, and the amplitude of both solitons is independent of H. The present investigation could be useful for researches on astrophysical plasmas as well as for ultra small micro- and nano- electronic devices