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The reductive perturbation approach was used to explore the nonlinear propagation of fast (compressive) and slow (rarefactive) electron–positron (EP) magnetoacoustic (EPMA) modes in an EP plasma medium. The solitary wave solution of the Korteweg-de Vries (K-dV) equation is used to identify the basic properties of EP compressional Alfvén waves. It is shown that the fast (slow) EPMA mode is predicted to propagate as compressive (rarefactive) solitary waves. The basic features (i.e., speed, amplitude, and width) of the compressive (i.e., fast) EPMA waves are found to be completely different from those of rarefactive (i.e., slow) EPMA ones. It is also examined that hump (dip) shape solitary waves are found for the fast (slow) mode. The significance of our findings is in understanding the nonlinear electromagnetic wave phenomena in laboratory plasma and space environments where EP plasma may exist.

The propagation of small amplitude stationary profile nonlinear solitary waves in a pair plasma is investigated by employing the reductive perturbation technique via the well-known Korteweg–de Vries (KdV) and modified KdV (mKdV) equations. This study tends to derive the exact form of nonlinear solutions and study their characteristics. Two distinct pair-ion species of opposite polarity and the same mass are considered in addition to a massive charged background species that is assumed to be stationary, and given the frequency scale of interest within the pair-ion context, the third species is thought of as a background defect (e.g., charged dust) component. On the opposite hand, the model conjointly applies formally to electron–positron–ion plasmas if one neglects electron–positron annihilation. A parametric analysis is carried out, with regard to the impact of the dusty plasma composition (background number density), species temperature(s), and background species. It is seen that distinguishable solitary profiles are observed for KdV and mKdV equations. The results are connected in pair-ion (fullerene) experiments and potentially in astrophysical environments of Halley’s comet and pulsar magnetosphere as well.

A theoretical investigation has been made on the propagation of ion-acoustic shock waves in a magnetized pair-ion plasma having inertial warm positive and negative ions and inertialess super-thermal electrons and positrons. The well known Burgers equation has been derived by employing the reductive perturbation method. The plasma model supports both positive and negative shock structures under consideration of super-thermal electrons and positrons. It is found that the oblique angle (δ) enhances the magnitude of the amplitude of both positive and negative shock profiles. It is also observed that the steepness of the shock profiles decreases with the kinematic viscosity of the ion and the height of the shock profile increases (decreases) with the mass of the positive (negative) ion. The implications of the results have been briefly discussed for space and laboratory plasmas.