Generalized analytical solutions of a Korteweg–de Vries (KdV) equation with arbitrary real coefficients: Association with the plasma-fluid framework and physical interpretation (original) (raw)
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Quantitative and qualitative analyses of the mKdV equation and modeling nonlinear waves in plasma
Frontiers in Physics
In this paper, nonlinear electrostatic structures on the ion time scale in plasma consisting of two populations of electrons (cold and hot), positrons, and warm adiabatic ions are investigated. The multiple scale method is used to derive the modified Korteweg–de Vries equation (mKdVE). The Jacobi elliptic function expansion method (JEFEM) is employed to find some exact analytical solutions such as periodic, solitonic, and shock solutions. It is shown that the variation in the plasma parameters of interest, for our model, allows the existence of solitary and periodic structures and no shocks. It is also shown that the most important plasma parameters for the plasma model under consideration are positron concentration, α, and the percentage of cold and hot electrons, represented by the parameters μ and ν, respectively. Additionally, the qualitative behavior of the mKdVE is studied using dynamical system theory. The topological structure of the solution is discussed in the phase plane....
Computational Solutions for the Korteweg–deVries Equation in Warm Plasma
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters to reveal different solutions, i.e. bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points called "blowup" solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.
Işık University Press, 2020
In this paper, the ion-acoustic wave is investigated in a plasma with qnonextensive electrons and two oppositely charged ions with varying masses. These parameters are found to modify the linear dispersion relation and nonlinear solitary structures. The reductive perturbation method is employed to derive modified Korteweg-de Vries (KdV) equation. To solve the obtained governing evolution equation, the exact solution in the planar geometry is obtained and used to obtain an analytical approximate progressive wave solution for the nonplanar evolution equation. The analytical approximate solution so obtained is compared with the numerical solution of the same nonplanar evolution equation and the results are presented in 2D and 3D figures. The results revealed that both solutions are in good agreement. A parametric study is carried out to investigate the effect of different physical parameters on the nonlinear evolution solution behavior. The obtained solution allows us to study the impact of various plasma parameters on the behavior of the nonplanar ion-acoustic solitons. The suitable application of the present investigations can be found in laboratory plasmas, where oppositely charged ions and nonthermal electrons dwell.
Results in Physics, 2020
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Nonlinear plasma waves excitation by intense ion beams in background plasma
Physics of Plasmas, 2004
Plasma neutralization of an intense ion pulse is of interest for many applications, including plasma lenses, heavy ion fusion, cosmic ray propagation, etc. An analytical electron fluid model has been developed to describe the plasma response to a propagating ion beam. The model predicts very good charge neutralization during quasi-steady-state propagation, provided the beam pulse duration b is much longer than the electron plasma period 2/ p , where p ϭ(4e 2 n p /m) 1/2 is the electron plasma frequency, and n p is the background plasma density. In the opposite limit, the beam pulse excites large-amplitude plasma waves. If the beam density is larger than the background plasma density, the plasma waves break. Theoretical predictions are compared with the results of calculations utilizing a particle-in-cell ͑PIC͒ code. The cold electron fluid results agree well with the PIC simulations for ion beam propagation through a background plasma. The reduced fluid description derived in this paper can provide an important benchmark for numerical codes and yield scaling relations for different beam and plasma parameters. The visualization of numerical simulation data shows complex collective phenomena during beam entry and exit from the plasma.
The reductive perturbation method has been employed to derive the Kadomstev- Petviashvili equation for small but finite amplitud electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KP equation. numerical studies have been made using plasma parameters reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called blowup solutions in addition to the propagation of an explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere
Quantum and Relativistic Effects on the KdV and Envelope Solitons in Ion-Plasma Waves
In this article, we investigate the linear and nonlinear behavior of ion-plasma waves in a two-component plasma containing ions and dust particles. We have studied the linear dispersion characteristics, nonlinear KdV solitons, and amplitude modulated electrostatic waves. Such ion-plasma wave modes in dust-ion plasma have been theoretically investigated by incorporating quantum diffraction and relativistic effects. Numerical analysis of the linear dispersion relation with variations of different parameters has been carried out. By employing the reductive perturbation technique the KdV equation describing the small amplitude solitary profile has been studied. Using the standard multiple scale perturbation method, a nonlinear Schrödinger (NLS) equation has been derived by including quantum and relativistic effects, which describes the nonlinear evolution of the ion-plasma waves in dust-ion plasma. The wave is found to become modulationally unstable beyond certain critical wavenumber. The critical wavenumber and the growth rate of modulational instability are shown to depend significantly on the relativistic motion of plasma particles and the quantum diffraction effect. The results presented in the article are expected to be helpful for understanding the propagation of finite amplitude ion-plasma waves in some laboratory and astrophysical plasma systems.
Propagation of Nonlinear Waves in Multicomponent Pair Plasmas and Electron-positron-ion Plasmas
AIP Advances (USA), 2022
The propagation of small amplitude stationary profile nonlinear solitary waves in a pair plasma is investigated by employing the reductive perturbation technique via the well-known Korteweg-de Vries (KdV) and modified KdV (mKdV) equations. This study tends to derive the exact form of nonlinear solutions and study their characteristics. Two distinct pair-ion species of opposite polarity and the same mass are considered in addition to a massive charged background species that is assumed to be stationary, and given the frequency scale of interest within the pair-ion context, the third species is thought of as a background defect (e.g., charged dust) component. On the opposite hand, the model conjointly applies formally to electron-positron-ion plasmas if one neglects electron-positron annihilation. A parametric analysis is carried out, with regard to the impact of the dusty plasma composition (background number density), species temperature(s), and background species. It is seen that distinguishable solitary profiles are observed for KdV and mKdV equations. The results are connected in pair-ion (fullerene) experiments and potentially in astrophysical environments of Halley's comet and pulsar magnetosphere as well.
Advances in Mathematical Physics, 2012
The reductive perturbation method has been employed to derive the Korteweg-de Vries KdV equation for small-but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called "blowup" solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.