Dust−ion acoustic freak wave propagation in a nonthermal mesospheric dusty plasma

El‐Labany, S. K.; El-Shewy, Ε. K.; El-Razek, H. N. Abd; El-Rahman, A.A.

doi:10.1134/s1063780x17050038

Cited by 17 publications

(18 citation statements)

References 35 publications

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“…To study the MI of DAWs, we will derive the NLSE by employing the standard multiple scale (reductive perturbation) technique . Let A be the state (column) vector ( n d , u d , ϕ ) T , describing the system's state at a given position x and instant t. We shall consider small deviations from the equilibrium state A (0) = (1, 0, 0) T by taking …”

Section: Derivation Of Nlsementioning

confidence: 99%

“…

A = A^{((), 0)} + ϵ A^{((), 1)} + ϵ^{2} A^{((), 2)} + \dots = A^{((), 0)} + {false\sum}_{n = 1}^{\infty} ϵ^{n} A^{((), n)},

where ϵ ≪ 1 is a smallness parameter. In the standard multiple scale (reductive perturbation) technique, the stretched (slow) space and time variables are commonly used by many authors as follows:

ξ = ϵ (x - v_{g} t), τ = ϵ^{2} t,

where v g is the group velocity in the x direction. We assume that all perturbed states depend on the fast scales via the phase θ 1 = kx − ωt only, while the slow scales enter the argument of the l th harmonic amplitude

A_{l}^{((), n)}

, which is allowed to vary along x ,

A^{((), n)} = {false\sum}_{l = - \infty}^{\infty} A_{l}^{((), n)} (ξ, τ) e^{il (kx - ω italict)} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…The reality condition

A_{- l}^{((), n)} = A_{l}^{(n) *}

is met by all state variables. According to these considerations, the derivative operators are treated as follows

\frac{\partial}{\partial t} \to \frac{\partial}{\partial t} - ϵ v_{g} \frac{\partial}{\partial ξ} + ϵ^{2} \frac{\partial}{\partial τ},

\frac{\partial}{\partial x} \to \frac{\partial}{\partial x} + ϵ \frac{\partial}{\partial ξ} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…According to these considerations, the derivative operators are treated as follows. [17][18][19][20][21][22][23][24][25][26][27]…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…Finally, the third harmonic modes (m = 3) and (l = 1), with the help of (16)- (27), give a set of equations, which can be reduced to the following NLSE:…”

Section: Derivation Of Nlsementioning

confidence: 99%

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Dust‐acoustic envelope solitons in super‐thermal plasmas

Noman

Chowdhury

Mannan

et al. 2019

Contributions to Plasma Physics

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The modulational instability (MI) of the dust‐acoustic waves (DAWs) in an electron‐positron‐ion‐dust plasma (containing super‐thermal electrons, positrons, and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the non‐linear Schrödinger equation (NLSE). To derive the NLSE, the reductive perturbation method was employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super‐thermal electrons, positrons, and ions significantly modifies both the stable and unstable regions. The critical wave number kc (at which MI sets in) depends on the super‐thermal electron, positron, and ion, and adiabatic dust concentrations.

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Section: Derivation Of Nlsementioning

confidence: 99%

“…

A = A^{((), 0)} + ϵ A^{((), 1)} + ϵ^{2} A^{((), 2)} + \dots = A^{((), 0)} + {false\sum}_{n = 1}^{\infty} ϵ^{n} A^{((), n)},

where ϵ ≪ 1 is a smallness parameter. In the standard multiple scale (reductive perturbation) technique, the stretched (slow) space and time variables are commonly used by many authors as follows:

ξ = ϵ (x - v_{g} t), τ = ϵ^{2} t,

A_{l}^{((), n)}

, which is allowed to vary along x ,

A^{((), n)} = {false\sum}_{l = - \infty}^{\infty} A_{l}^{((), n)} (ξ, τ) e^{il (kx - ω italict)} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…The reality condition

A_{- l}^{((), n)} = A_{l}^{(n) *}

is met by all state variables. According to these considerations, the derivative operators are treated as follows

\frac{\partial}{\partial t} \to \frac{\partial}{\partial t} - ϵ v_{g} \frac{\partial}{\partial ξ} + ϵ^{2} \frac{\partial}{\partial τ},

\frac{\partial}{\partial x} \to \frac{\partial}{\partial x} + ϵ \frac{\partial}{\partial ξ} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…According to these considerations, the derivative operators are treated as follows. [17][18][19][20][21][22][23][24][25][26][27]…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…Finally, the third harmonic modes (m = 3) and (l = 1), with the help of (16)- (27), give a set of equations, which can be reduced to the following NLSE:…”

Section: Derivation Of Nlsementioning

confidence: 99%

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