## 1 Introduction
At these stages, the non-Maxwellian velocity distribution functions are an arena for obtaining the electron density function when the electron energy is higher/less than the isothermal energies or the electron energy becomes nonthermal. For instance, the \(q-\) velocity distribution function [27] is very suitable to describe the particles system consisting of a very huge number of both low and high speed because of the long rang nature of Colombian interactions with the presence of sub-thermal and superthermal particles in the plasma environments. Besides, one can use the \(\alpha\) (Cairns)-velocity distribution [28] for electrons because the lighter particles (electrons) have a great potential to be trapped in the potential wall due to its high energy rather than other plasma species (positive or negative ions). [PERSON] et al. [29] have already described IA modulation instability characteristics in negative ion plasma having nonthermal electrons. They have also shown that the instability conditions affected by nonthermal electron parameters in D and F regions in Earth's ionosphere. It is therefore suggested to extend the hydrodynamic fluid model by considering \((\alpha,q)\)-distributed electrons [25] and pair-ions because the \((\alpha,q)\) velocity distribution function is not only used for superthermal, subthermal, and nonthermal, but also Maxwellian distributed electrons. On the other hand, the most credible mechanism is the production of shock waves phenomena because they propagate superficial. Basically, the IA shock wave is generated in plasmas due to the comparative speed between the rarefaction wave and ambient plasma exceeds IA acoustic speed, where the concentration of the rarefaction wave and ambient medium are almost analogous. Owing to the significance of IA shock wave for understanding the physical issues in many environments, such wave phenomena have been studied by many researchers by considering different types of plasma environments [22; 23; 30; 31]. In [32; 33], the authors have confirmed the production of shock waves in the Q-machine with negative ions. [PERSON] et al. [34; 35] have reported the nonlinear IA shock in a pair-ion (\(C_{60}^{+},C_{60}^{-}\)) plasma by deriving the Korteweg-de Vries equation Burgers equation (KdVBE) with the presence of weakly dissipative media. Further, the \(N\)-wave phenomena may interact with each other in two different ways. One of which is the overtaking phenomenon, where \(N\)-wave moves along the same direction and the other one is the face-to-face collision, where the angle between two propagation directions among \(N\)-wave is \(\pi\). Very recently, [PERSON] [36] has been reported the face-to-facecollisions of an IA multi-soliton described by two-sided KdVEs in a dense plasma. [PERSON] and [PERSON] [37] have reported the overtaking collisions of electrostatic \(N\)-soliton described by KdVE in electron--hole quantum plasmas. In addition, [PERSON] et al. [38] have theoretically described the nonlinear IA single shock waves via KdVE in negative ion plasmas with \(q\)-distributed electrons by stretching the kinematic viscosity coefficient parameter of negative and positive ions as \(\eta_{+}=\epsilon^{1/2}\eta_{+0}\) and \(\eta_{-}=\epsilon^{1/2}\eta_{-0}\), respectively. Very recently, [PERSON] and [PERSON] [30] have investigated the face to face collision phenomena between two IA single-shock waves via the stationary solutions of two-sided KdVEs in a plasma system having pair-ion and isothermal electrons. They have also considered the stretching of kinematic viscosity coefficients for negative and positive ions as \(\eta_{1i}=\epsilon^{1/2}\eta_{1}\) and \(\eta_{2i}=\epsilon^{1/2}\eta_{2}\), respectively. [PERSON] [39] has clearly shown that the stretching of kinematic viscosity coefficient parameters is not usually valid. The valid stretching coordinates supported only the Burgers equation, which divulges the formation of shock structures in the plasmas.