On the evolution of nonlinear ion-acoustic solitary waves in electron–positron–ion plasma within nonthermal energy distribution: Elucidating the influence of the geometry and composition on the waves’ existence, amplitude, and stability

The evolution of ion-acoustic waves (IAWs) in a nonlinear one-dimensional planar geometry within a curved framework is examined in a plasma that comprises positrons, inertial ions, and ( 𝑟 , 𝑞 ) -distributed electrons. To assess departures from the behavior of planar waves, cylindrical and spherical configurations are considered. Particularly, a nonplanar modified Korteweg–de Vries (mKdV) equation, which is a generalized form of the standard mKdV equation that incorporates the effects of cylindrical or spherical geometry on nonlinear wave propagation and describes weakly nonlinear ion-acoustic perturbations, is derived via the employment of the reductive perturbation method (RPM). When plasma parameters cause the quadratic nonlinear coefficient to vanish, the standard Korteweg–de Vries (KdV) model is insufficient. In these circumstances, the mKdV equation controls the wave behavior, and it is primarily characterized by a cubic nonlinear term. This nonlinearity property modifies the amplitude variations, improves nonlinear steepening and wave polarity, leading to a more solid picture of IAWs around critical conditions. The progressive wave solutions of the derived nonplanar mKdV equation are found via the modified weighted residual procedure. This semi-analytical procedure offers approximate analytical solutions for the electrostatic potential, empowering the examination of the time evolution of solitary-wave amplitude, width, and propagation features in planar, cylindrical, and spherical geometries. The effects of two significant parameters that greatly affect the KdV/mKdV equation’s coefficients, and consequently the characteristics of these waves, specifically the electron-to-positron temperature ratio and positron concentration, along with the double ( 𝑟 , 𝑞 ) spectral indices on the features of IAWs, are examined through numerical methods. Numerical experimentation reveal that deviations from Maxwellian distributions caused by the ( 𝑟 , 𝑞 ) parameters greatly impact the amplitude, width, and stability of solitary waves. Additionally, nonplanar geometry introduces dispersive effects that can either enhance or weaken wave localization. This research offers insights into the nonlinear behavior of IAWs in astrophysical, space, and laboratory plasmas, where considering generalized particle distributions and geometric effects is essential for understanding wave propagation. This study is distinctive as it represents the inaugural instance where double ( 𝑟 , 𝑞 ) spectral parameters for both positrons and electrons are incorporated within the nonplanar mKdV context for electron–positron–ion (EPI) plasmas. Unlike earlier investigations limited to single spectral parameter distributions (e.g., kappa or Tsallis), planar geometries, or simpler models, current work unveils how curvature-induced dispersive impacts interact with non-Maxwellian deviations to modify solitary wave amplitude, width, and stability, especially around critical plasma conditions where quadratic nonlinearity ceases to exist. Numerical outcomes reveal that ( 𝑟 , 𝑞 ) factors and nonplanar geometry significantly modulate wave steepening and localization, offering new physical insights for real-world EPI plasmas. Altogether, the results presented herein reveal that wave amplitude reduces with evolution time, while geometric impacts cause stronger amplitude decrement in spherical configurations compared to cylindrical and planar ones. Rising electron-to-positron temperature ratio and positron concentration, as well as bigger values of the spectral parameters 𝑟 and 𝑞 , result in wider and lower-amplitude waves. These results offer profounder insights into the nonlinear behavior of IAWs in astrophysical, space, and laboratory plasmas, where generalized particle distributions and geometric impacts are crucial for a complete understanding of wave evolution.