Shock, Solitary, and Periodic Wave Solutions of the Ion Acoustic Waves for Nonextensive Dusty Plasma in the Framework of Korteweg-de Vries-Burgers Equation with Forcing and Damping Terms

The primary purpose of this article is to explore different types of wave solutions such as shock, solitary, and periodic solutions for the ion acoustic waves (IAWs) propagating in a collisional dusty plasma containing dust grain with a negative charge, positive ions, neutral particles, and electrons abiding q-nonextensive velocity distribution. To observe IAW in a plasma medium under the influence of externally applied periodic force, the forced Korteweg-de Vries-Burgers (FKdVB) equation is formally derived from the governing basic equations utilizing reductive perturbation technique (RPT). From the modified tanh method (MTM), some exact analytical solutions are derived based on some relation between the coefficients in the equation, from which the impact of different physical parameters on wave propagation is discussed from a numerical perspective. Apart from this, propagation of IAW is also studied separately considering the dust ion collision effect. To check the behaviors of IAW in a collisional plasma, the damped Korteweg-de Vries-Burgers (DKdVB) equation is already derived in an earlier literature in which using conservation law, only the solitary wave solution is derived for small burgers term. The presence of burgers term necessarily initiates the existence of shock waves. In order to search shock solution, the method of undetermined coefficient (MUC) and the Exp-function method (EFM) is employed, and new type of solitary wave, shock wave, and periodic wave solutions is explored. The obtained new solutions extend earlier results and aid effectively in understanding wave properties. Some numerical graphs are depicted to investigate the nonlinear properties of IAW with the variance of physical plasma parameters.