In this paper, we have studied the propagation of non-linear ion-acoustic waves in a plasma comprising of (r, q)-distributed electrons and kappa-distributed positrons. We have investigated the effect of complete electron distribution profile on the propagation of small, as well as arbitrary, amplitude solitons (via pseudopotential technique) by using generalized (r, q) distribution, which exhibits a spiky and flat top nature at low energies and a super-thermal tail at high energies. Interestingly, for negative values of r, solitons are formed with both polarities, positive (compressive) and negative (rarefactive), separately within a small amplitude limit and exist simultaneously in an arbitrary amplitude limit. We also found that the propagation of solitons has been affected by the change in parameters r, q, positron concentration, and electron to positron temperature ratio. The results presented in this study add to the fundamental understanding of the complete profile of the electron distribution function, highand low-energy parts, and in the formation of compressive and rarefactive small and finite amplitude solitons in both space and astrophysical plasmas.

The influence of the low energy part of the velocity distribution on the propagation characteristics of the nonlinear ion-acoustic waves is investigated in this study by employing the double spectral index (r, q) distribution function. We present an ample study to ascertain how the formation of compressive and rarefactive ion-acoustic solitary structures is influenced by the low energy particles in the distribution profile. We found that only compressive structures are formed for flat top distribution; however, both compressive and rarefactive structures are admissible for spiky distribution. The effect of spectral indices r and q on the formation of solitary structures is explored in detail, and a brief comparison with the Maxwellian and kappa distribution is also given. The present study is imperative in understanding the role of flat top or spiky distributions in plasmas, where positrons are present, and simultaneous observations of such distributions.