Ion Acoustic Shock Wave Excitations Around the Critical Values in an Unmagnetized Pair–Ion Plasma

This work deals with the ion-acoustic shock waves (IASWs) around the critical values in an unmagnetized pair–ions plasma with ( $$\alpha , q$$ )-distributed electrons by formulating the correct stationary solution of Burgers-type equations with higher-order corrections. By considering higher-order correction of the reductive perturbation technique, the modified Burgers(mB)-, and mixed modified Burgers(mmB)-type equations are derived. With the changes of viscosity coefficients of positive and negative ions, the electrostatic IASWs and normalized electric fields are investigated around the critical values. The current studies might be very useful to understand the behavior of shocks around the critical values in the F- and D-regions of Earth’s ionosphere, and the later experimental verification in plasma laboratory.