On the electrostatic solitary waves in an electron–positron–ion plasma with Cairns–Tsallis distributed electrons

The propagation of nonlinear electrostatic low-frequency ion-acoustic solitary waves (SWs) in an electron–positron–ion non-Maxwellian plasma with Cairns–Tsallis-distributed electrons and thermal positrons is examined in this work. The reductive perturbation technique (RPT) reduces the fluid model equations to the Korteweg–de Vries (KdV) equation family, including the planar KdV, modified KdV (mKdV), Kawahara, and modified Kawahara equations. Analysis of the present model’s polarity, based on the sign of the quadratic nonlinear term’s coefficient in the KdV equation, reveals the presence of both compressive and rarefactive nonlinear structures. This implies that, under specific plasma parameter values, the coefficient of the quadratic nonlinear term of the KdV equation will vanish. Therefore, we proceed to formulate an additional evolution equation with higher-order nonlinearity, known as the modified KdV (mKdV) equation, to characterize the nonlinear structures at specific critical values of the plasma parameters. Moreover, we investigate the results using the Kawahara and modified Kawahara equations, also known as the generalized fifth-order KdV and mKdV equations, as they can aid in reducing the discrepancy between the theoretical results of the KdV and mKdV equations and specific laboratory results or space observations. We analyze how the nonextensive parameter, nonthermal parameter (nonthermality), and positron concentration influence the properties of the SW structures. This research has potential applications in space and astrophysical plasma physics like interstellar plasma, stellar polytropes, and pulsar magnetosphere.