Exploring non-Maxwellian distributions effects on modulational instability and rogue wave triplets in ion-acoustic plasmas

This study explores the implications of non-Maxwellian electron distributions on modulational instability and the formation of ion-acoustic rogue wave triplets in unmagnetized collisionless plasma. We employ the reductive perturbation technique to derive the nonlinear Schr & ouml;dinger equation from a fluid model that incorporates these non-Maxwellian electron distributions. This framework enables a comprehensive analysis of the modulational instability of ion-acoustic waves, characterized by the ratio of dispersion and nonlinear coefficients within the nonlinear Schr & ouml;dinger equation. The injection of nonthermal electrons and spectral indices via qn-nonextensive nonthermal and generalized (r, q) distribution functions significantly influences the onset of modulational instability and its corresponding growth rate, providing critical insights into the dynamic behavior of the plasma system. These distribution functions facilitate the identification of dark and bright solitons in stable and unstable regions, respectively. Furthermore, we incorporate multiple physical free parameters that affect the formation of rogue wave triplets. Remarkably, our findings reveal that these parameters in the second-order rogue wave solution lead to three distinct peaks arranged in a triangular pattern accompanied by a novel rotation of these peaks. We have thoroughly investigated the existence regions of both dark and bright envelope solitons, which correspond to the modulationally unstable and stable regimes of ion- acoustic waves, respectively. Our study explores into the criteria that govern the formation of these solitons, elucidating their unique features in the context of the stability dynamics of the plasma's wave system. This systematic analysis enhances our understanding of the properties of ion-acoustic solitary waves that may arise in non-Maxwellian space plasmas, paving the way for future research in this area.