Abstract
A strongly coupled quantum dusty plasma consisting of electrons and dust with the ions in the background is considered when there is streaming of electrons. It is observed that the streaming gives rise to both the slow and fast modes of propagation. The nonlinear mode is then analyzed by the reductive perturbation approach, resulting in the KdV-equation. In the critical situation where non-linearity vanishes, the modified scaling results in the MKdV equation. It is observed that both the KdV and MKdV equations possess quasi-solitary wave solution, which not only has the character of a soliton but also has a periodic nature. Such types of solitons are nowadays called nanopteron solitons and are expressed in terms of cnoidal-type elliptic functions.
Highlights
The interest in study of plasmas containing dust particles are growing day by day, because of the importance of such plasmas in the study of the space environment, such as asteroid zones, planetary rings, cometary tails as well as lower ionosphere of earth
We have shown how an electron streaming in a quantum strongly coupled dusty plasma can generate both ‘slow’ and ‘fast’ modes in the plasma
Earlier this type of phenomenon was studied by Shukla et al [25] but that model did not take into account the quantum effects or strong coupling but the effect of the magnetic field
Summary
The interest in study of plasmas containing dust particles are growing day by day, because of the importance of such plasmas in the study of the space environment, such as asteroid zones, planetary rings, cometary tails as well as lower ionosphere of earth. One can show that when the temperature approaches the electron Fermi temperature TFe , the equilibrium distribution function changes from the Maxwell–Boltzmann ∝ exp(− E/k B T ) to the Fermi–Dirac one Another important domain of present day plasma physics is the study of dusty plasma [12], and many analyses have been performed on quantum dusty plasma [13,14]. The corresponding investigation has been performed at least in two main formulations: one is to use the visco-elastic model [20] and the other by using effective electrostatic pressure [21] It was Ikezi [22] who predicted that a dusty plasma can enter the strong coupling regime due to high charge and low temperature of the dust that makes the coupling co-efficient Γ 1, and the coupling co-efficient e2 Z 2. Such an equation is observed to posses a cnoidal-type soliton
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