Homotopy perturbation method for modeling electrostatic structures in collisional plasmas

Kashkari, Bothayna S.; El-Tantawy, S. A.

doi:10.1140/epjp/s13360-021-01120-9

Cited by 29 publications

(8 citation statements)

References 40 publications

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“…It is noted that we calculate the results only up to two terms for obtaining the smooth solitary wave solution of equation (17) with initial condition (25). In Figure 3, we provide the graphical comparison between the obtained results of L T-HPM and the exact solution at −5 ≤ x ≤ 5 and t 1.…”

Section: U(x T)mentioning

confidence: 99%

“…Another powerful technique was introduced to solve the nonlinear problem by He [23,24] with some recent developments. Kashkari and El-Tantawy [25] applied the homotopy perturbation method for the dissipative soliton collisions in a collisional complex unmagnetized plasma. Later many authors showed the validity and accuracy of this approach [26,27].…”

Section: Introductionmentioning

confidence: 99%

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A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

Fang

Nadeem

Wahash

2022

Journal of Mathematics

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This paper presents the approximate solution of the nonlinear acoustic wave propagation model is known as the modified Camassa–Holm (mCH) equation with the Caputo fractional derivative. We examine this study utilizing the Laplace transform ( ℒ T) coupled with the homotopy perturbation method (HPM) to construct the strategy of the Laplace transform homotopy perturbation method ( ℒ T-HPM). Since the Laplace transform is suitable only for a linear differential equation, therefore ℒ T-HPM is the suitable approach to decompose the nonlinear problems. This scheme produces an iterative formula for finding the approximate solution of illustrated problems that leads to a convergent series without any small perturbation and restriction. Graphical results demonstrate that ℒ T-HPM is simple, straightforward, and suitable for other nonlinear problems of fractional order in science and engineering.

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Section: U(x T)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

Fang

Nadeem

Wahash

2022

Journal of Mathematics

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“…However, in the absence of collision (i.e.,

ν = 0

), the modified KdV equation has a straightforward analytical solution [ 60 ] as

ψ^{'} false(ξ, τ false) = {normalΨ}^{'} sech (\frac{ξ - U_{0} τ}{L^{'}}),

where amplitude and width are defined as

{normalΨ}^{'} = \sqrt{6 U_{0} / α^{'}}

and

L^{'} = \sqrt{β / U_{0}}

. As there is no exact analytical solution for dmKdV, we have followed the semi‐analytical approach of Kashkari et al [ 39 ] and developed the following solution

ψ_{ν}^{'} false(ξ, τ false) = {normalΨ}_{m}^{'} sech (\frac{Θ^{'} (τ)}{L^{'} (τ)}),

where

\begin{array}{l} Θ^{'} (τ) = ξ - italicUH (τ), \\ H (τ) = \frac{2}{3 ν} e^{- ν τ} ((), e^{\frac{3 ν}{2} τ} - 1), \\ ψ_{m}^{'} (τ) = ψ_{m}^{'} (0) e^{- ν τ}, \\ L^{'} (τ) = L^{'} (0) e^{ν} \end{array}

…”

Section: Damped Diasws: Perturbative Approachmentioning

confidence: 99%

“…There is always a chance for the solitary pulses to get damped due to dissipation in the plasma medium gradually. Apart from the existence of the collision between different plasma components, [ 37–39 ] the ion‐acoustic solitary structures can also get dissipated if the ions no longer remain cold instead become hot enough compared to that of the electron species, that is, due to the ion temperature effect. [ 40–43 ] As most of the practical systems around us are not in equilibrium, almost every wave has to suffer a certain amount (more or less) of dissipation.…”

Section: Introductionmentioning

confidence: 99%

Damped dust‐ion‐acoustic solitons in collisional magnetized nonthermal plasmas

Hassan

Sultana

2021

Contributions to Plasma Physics

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A multispecies magnetized collisional nonthermal plasma system, containing inertial ion species, noninertial electron species following nonthermal κ‐distribution, and immobile dust particles, is considered to examine the characteristics of the dissipative dust‐ion‐acoustic soliton modes, theoretically and parametrically. The electrostatic solitary modes are found to be associated with the low‐frequency dissipative dust‐ion‐acoustic solitary waves (DIASWs). The ion‐neutral collision is taken into account, and the influence of ion‐neutral collisional effects on the dynamics of dissipative DIASWs is investigated. It is reported that most of the plasma medium in space and laboratory are far from thermal equilibrium, and the particles in such plasma system are well fitted via the κ‐nonthermal distribution than via the thermal Maxwellian distribution. The reductive perturbation approach is adopted to derive the damped KdV (dKdV) equation, and the solitary wave solution of the dKdV equation is derived via the tangent hyperbolic method to analyse the basic features (amplitude, width, speed, time evolution, etc.) of dissipative DIASWs. The propagation nature and also the basic features of dissipative DIASWs are seen to influence significantly due to the variation of the plasma configuration parameters and also due to the variation of the supethermality index κ in the considered plasma system. The implication of the results of this study could be useful for better understanding the electrostatic localized disturbances, in the ion length and time scale, in space and experimental dusty plasmas, where the presence of excess energetic electrons and ion‐neutral collisional damping are accountable.

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“…All these families were used for describing the unmodulated solitons that propagate with phase velocity and with smooth crest. Moreover, the solitary waves that have been described by these families of equations preserve their shapes, velocities, amplitudes, energies after collisions [ 1 , 2 , 25 – 27 ]. Moreover, these family do not accommodate wave breaking [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics

2021

Self Cite

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In this work two kinds of smooth (compactons or cnoidal waves and solitons) and nonsmooth (peakons) solutions to the general Degasperis-Procesi (gDP) equation and its family (Degasperis-Procesi (DP) equation, modified DP equation, Camassa-Holm (CH) equation, modified CH equation, Benjamin-Bona-Mahony (BBM) equation, etc.) are reported in detail using different techniques. The single and periodic peakons are investigated by studying the stability analysis of the gDP equation. The novel compacton solutions to the equations under consideration are derived in the form of Weierstrass elliptic function. Also, the periodicity of these solutions is obtained. The cnoidal wave solutions are obtained in the form of Jacobi elliptic functions. Moreover, both soliton and trigonometric solutions are covered as a special case for the cnoidal wave solutions. Finally, a new form for the peakon solution is derived in details. As an application to this study, the fluid basic equations of a collisionless unmagnetized non-Maxwellian plasma is reduced to the equation under consideration for studying several nonlinear structures in the plasma model.

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Homotopy perturbation method for modeling electrostatic structures in collisional plasmas

Cited by 29 publications

References 40 publications

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

Damped dust‐ion‐acoustic solitons in collisional magnetized nonthermal plasmas

Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics

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