Homotopy perturbation method for studying dissipative nonplanar solitons in an electronegative complex plasma

Kashkari, Bothayna S.; El-Tantawy, S. A.; Salas, Alvaro H.; El‐Sherif, L. S.

doi:10.1016/j.chaos.2019.109457

Cited by 66 publications

(21 citation statements)

References 46 publications

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“…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.…”

Section: Quantum Plasma Oscillationsmentioning

confidence: 99%

“…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].…”

Section: Quantum Plasma Oscillationsmentioning

confidence: 99%

“…e soliton solution to equation (47) in the form of the Weierstrass elliptic function ℘ could be written in the following manner:…”

Section: Quantum Plasma Oscillationsmentioning

confidence: 99%

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

Salas

Alharthi

2021

Mathematical Problems in Engineering

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This paper presents some novel solutions to the family of the Helmholtz equations (including the constant forced undamping Helmholtz equation (equation (1)) and the constant forced damping Helmholtz equation (equation (2))) which have been reported. In the beginning, equation (1) is solved analytically using two different techniques (direct and indirect solutions): in the first technique (direct solution), a new assumption is introduced to find the analytical solution of equation (1) in the form of the Weierstrass elliptic function with arbitrary initial conditions. In the second case (indirect solution), the solution of the undamping (standard) Duffing equation is devoted to determine the analytical solution to equation (1) in the form of Jacobian elliptic function with arbitrary initial conditions. Moreover, equation (2) is solved using a new ansatz and with the help of equation (1) solutions. Also, the evolution equations (equations (1) and (2)) are solved numerically via the Adomian decomposition method (ADM). Furthermore, a comparison between the approximate analytical solution and approximate numerical solutions using the fourth-order Runge–Kutta method (RK4) and ADM is reported. Furthermore, the maximum distance error for the obtained solutions is estimated. As a practical application, the Helmholtz-type equation will be derived from the fluid governing equations of quantum plasma particles with(out) taking the ionic kinematic viscosity into account for investigating the characteristics of (un)damping oscillations in a degenerate quantum plasma model.

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Section: Quantum Plasma Oscillationsmentioning

confidence: 99%

Section: Quantum Plasma Oscillationsmentioning

confidence: 99%

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

Salas

Alharthi

2021

Mathematical Problems in Engineering

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“…A large number of researchers have studied the dynamics of the IAWs experimentally and theoretically in the last few decades [3][4][5][6][7][8][9][10]. There are many approaches for investigation the different types of nonlinear structures in plasma physics such as a reductive perturbation technique (RPT), Sagdeev potential approach, etc.…”

Section: Introductionmentioning

confidence: 99%

Linear and Nonlinear Electrostatic Excitations and Their Stability in a Nonextensive Anisotropic Magnetoplasma

et al. 2021

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In the present work, the propagation of (non)linear electrostatic waves is reported in a normal (electron–ion) magnetoplasma. The inertialess electrons follow a non-extensive q-distribution, while the positive inertial ions are assumed to be warm mobile. In the linear regime, the dispersion relation for both the fast and slow modes is derived, whose properties are analyzed parametrically, focusing on the effect of nonextensive parameter, component of parallel anisotropic ion pressure, component of perpendicular anisotropic ion pressure, and magnetic field strength. The reductive perturbation technique is employed for reducing the fluid equation of the present plasma model to a Zakharov–Kuznetsov (ZK) equation. The parametric role of physical parameters on the characteristics of the symmetry planar structures such solitary waves is investigated. Furthermore, the stability of the pulse soliton solution of the ZK equation against the oblique perturbations is investigated. Furthermore, the dependence of the instability growth rate on the related physical parameters is examined. The present investigation could be useful in space and astrophysical plasma systems.

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“…Then, this method has been extended by many other researchers for solving different problems. The HPM was applied to find the approximate analytical solution of the Allen-Cahn equation in [28], to study the maximum power extraction from fractional order doubly fed induction generator based wind turbines in [29], dissipative nonplanar solitons in an electronegative complex plasma in [30] and others [31][32][33]. Convergence of the parameter continuation method in the homotopy method based on the theorem of V.A.…”

Section: Introductionmentioning

confidence: 99%

Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

Noeiaghdam

Dreglea

et al. 2020

Symmetry

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This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method.

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Homotopy perturbation method for studying dissipative nonplanar solitons in an electronegative complex plasma

Cited by 66 publications

References 46 publications

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

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

Linear and Nonlinear Electrostatic Excitations and Their Stability in a Nonextensive Anisotropic Magnetoplasma

Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

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