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Abstract
A theoretical study is presented on the nonlinear self modulation of low
frequency electrostatic dust acoustic (DA) waves propagating in a strongly coupled
dusty plasma (SCDP) in the hydrodynamic regime. Using the derivative expansion
perturbation method, the basic equations are reduced to a nonlinear Schr ̈ dinger
type (NLST) equation describing the modulated dust acoustic waves. The
modulation (in) stability (MI) and the dependence of the system physical
parameters (angular frequency and group velocity) on the polarization force
variation have been examined. Moreover, the extended Poincar ́ -Lighthill Kuo
(PLK) technique is used to investigate the head-on collision (HoC) between two
DA dark solitons. The analytical phase shifts and the trajectories of these dark
solitons after the collision are derived. The numerical calculations illustrate that the
polarization effect has a strong influence on the nature of the phase shifts and the
trajectories of the two DA dark solitons after collision.
Futhermore, we investigated the MI of DAWs in a strongly coupled dust
plasma in the kinetic regime considering the variable dust charge. Employing the
derivative expansion perturbation technique, NLST equation, which governs the
MI of DAW, is obtained. Also, the characteristics of the HoC between two dark
solitons have been investigated theoretically in this regime. Using the extended
PLK technique, the analytical phase shifts after the HoC of two dark solitons
occurs are derived. It is found that the presence of the viscosity and the dust charge
variation as well as variation of relaxation time significantly modify the domain of
the MI and the HoC characteristics.
The present study is helpful in investigating nonlinear interaction and the
HoC of two DA solitary waves observed in recent dusty plasma experiments.