Abstract
In this paper, expressions of number densities for electron trapping for generalized (r, q), kappa, and Cairns distribution functions, respectively, are reported using the approach adopted by Landau and Lifshitz for Maxwellian trapping of electrons. For illustrative purposes, dispersive and dissipative equations for ion-acoustic waves are obtained in the presence of non-Maxwellian trapped electrons in the small amplitude limit. The solutions of the modified dispersive and dissipative nonlinear equations are reported, and a graphical analysis is given to present a detailed comparison of non-Maxwellian and Maxwellian trapping. The results presented here, to the best of authors' knowledge, are a first attempt of this kind. It is expected that the present investigation will unravel new horizons for future research and encourage the researchers to search for the nonlinear structures presented in this paper in the satellite data.