Simulation study on nonlinear structures in nonlinear dispersive media

In this work, the dynamic mechanism scenario of nonlinear electrostatic structures (unmodulated and modulated waves) that can propagate in multi-ion plasmas with the mixture of sulfur hexafluoride and argon gas is reported. For this purpose, the fluid equations of the multi-ion plasma species are reduced to the evolution (nonplanar Gardner) equation using the reductive perturbation technique. Until now, it has been known that the solution of nonplanar Gardner equation is not possible and for stimulating our data, it will solve numerically. At that point, the present study is divided into two parts: the first one is analyzing planar and nonplanar Gardner equations using the Adomian decomposition method (ADM) for investigating the unmodulated structures such as solitary waves. Moreover, a comparison between the analytical and numerical simulation solutions for the planar Gardner equation is examined, showing how powerful the ADM is in finding solutions in the short domain as well as its fast convergence, i.e., the approximate solution is consistent with the analytical solution for the planar Gardner equation after a few iterations. Second, the modulated envelope structures such as freak waves (FWs) are investigated in the framework of the Gardner equation by transforming this equation to the nonlinear Schrödinger equation (NLSE). Again, the ADM is used to solve the NLSE for studying FWs numerically. Furthermore, the effect of physical parameters of the plasma environment (e.g., Ar⁺-SF₅ ⁺-F^--SF₅ ^- plasma) on the characteristics of the nonlinear pulse profile is elaborated. These results help in a better understanding of the fundamental mechanisms of fluid physics governing the plasma processes.