Simulation study on nonlinear structures in nonlinear dispersive media

Abstract

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.

On the Approximate Solutions of the Constant Forced (Un)Damping Helmholtz Equation for Arbitrary Initial Conditions

“…In this section, we will reduce the fluid governing equations of a quantum plasma model to an evolution equation using the RPT [45][46][47][48][49]. After a suitable transformation, we will be able to convert the obtained evolution equation to a Helmholtz-type equation in order to investigate the characteristics behavior of the damping oscillations in the model under consideration.…”

“…By substituting stretching (42) and expansions (43) into system (40) and by collecting the terms of different powers of ε, we could get a system of reduced equations. Solving the system of reduced equations for the first-two orders of ε by following the same procedures in [46][47][48][49], we finally obtain the Korteweg-de Vries Burgers (KdVB) equation [50].…”

“…where C is the integration constant, c � − C p /(2B p ), α � V f /B p , and β � A p /(2B p ). Now, we can apply the above solution of the constant forced and damped Helmholtz equation that is given in equation ( 26) to equation (46) for investigating the characteristics of the damped oscillations in a quantum plasma.…”

“…Here, the obtained approximate analytical solution (26) to the constant forced and damped Helmholtz equation (46) will be analyzed numerically according to the quantum plasma parameters (T, η) � (0.1, 0.055), i.e., (α, β, c, F) � (1.828, 2.98, − 0.05, F), and (T, η) � (0.9, 0.18), i.e., (α, β, c, F) � (1.146, 1.7273, − 0.1, F).…”

The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

“…One of the most important characteristics is that the RWs are localized in space-time [12]. Also, their amplitude may be equal to three times of the adjacent/carrier amplitudes (we mean here the first-order RWs but the super RWs have amplitudes higher than 3 times the surrounding waves [13,[22][23][24]). Physically, these types of huge waves suck high energy from the surrounding pulses, which amplifies their amplitude.…”