Solitary ion-acoustic wave propagation in the presence of electron trapping and background nonextensivity

► Solitary ion-acoustic wave propagation in the presence of electron trapping is investigated within the theoretical framework of the Tsallis statistical mechanics. ► A physically meaningful Schamel-like distribution is outlined. ► In the small amplitude limit, the nonlinear dispersion relation is derived to analyze the global dependency of the main solitary wave quantities.