Abstract
The presence and propagation of dust-acoustic solitary waves in dusty plasma contains four components such as negative and positive dust species beside ions and electrons are studied. Both the ions and electrons distributions are represented applying nonextensive formula. Employing the reductive perturbation method, an evolution equation is derived to describe the small-amplitude dust-acoustic solitons in the considered plasma system. The used reductive perturbation stretches lead to the nonlinear KdV and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. This study represents that the presence of compressive or/and rarefactive solitary waves depends mainly on the value of the first-order nonlinear coefficient. The structure of envelope wave is undefined for first-order nonlinear coefficient tends to vanish. The coexistence of the two types of solitary waves appears by increasing the strength of nonlinearity to the second order using the modified KdV equation.
Highlights
Employing the reductive perturbation method, an evolution equation is derived to describe the smallamplitude dust-acoustic solitons in the considered plasma system. e used reductive perturbation stretches lead to the nonlinear Kortweg-de Vries (KdV) and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. is study represents that the presence of compressive or/and rarefactive solitary waves depends mainly on the value of the firstorder nonlinear coefficient. e structure of envelope wave is undefined for first-order nonlinear coefficient tends to vanish. e coexistence of the two types of solitary waves appears by increasing the strength of nonlinearity to the second order using the modified KdV equation
Since the existence of the dust charged particles was not neglected, because they modify the spectra of the plasma and they introduce new eigenmodes such as dust ion acoustic waves (DIAWs), dust acoustic waves (DAWs), dust lattice waves (DLWs), dust cyclotron acoustic, and dust dri mode, etc. [ – ]
They studied the same dusty plasma with vortexlike or nonthermal distribution for ions [ ]. ey concluded that the small amplitude dynamics of this system were described via the modified Kortweg-de Vries equation
Summary
A system of dusty plasma composed of ions and electrons with nonextensive distributions along with negative and positive dust sorts is treated in the following. e onedimensional fluid equations that depict this kind of plasma are represented as [ , – ]:. A system of dusty plasma composed of ions and electrons with nonextensive distributions along with negative and positive dust sorts is treated in the following. E onedimensional fluid equations that depict this kind of plasma are represented as [ , – ]:. + μpNp (x, t) = 0, where μe = Ne0/(Nn0Zn), μi = Ni0/(Nn0Zn), and μp = Np0Zp/(Nn0Zn) satisfy the neutrality condition μp + μi − μe = 1, where Ni0 and Ne0 are the equilibrium density values of ions and electrons, respectively. Ni(x, t) and Ne(x, t) are the ions and electrons fluid densities, which are taken by qnonextensive distribution forms as. Where the subscript l refers to i for ions and e for electrons, σi = −1, σe = Ti/Te and Te is the electrons temperature. Equations ( a)-( ) are complicated coupled nonlinear partial differential equations, so the reductive-perturbation method will be employed to discuss the acoustic waves of small-amplitude through our system of plasma
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