Abstract
We report the modifications in the propagation characteristics of dust acoustic solitary waves (DASWs) due to the polarization force acting on micron-size dust particles in a non-uniform plasma. In the small amplitude limit, we derive a K–dV-type equation and show that there is an increase in the amplitude and a reduction in the width of a solitary structure as the polarization force is enhanced for a given Mach number. For arbitrary amplitude waves we employ the Sagdeev potential method and find that the range of Mach numbers where solitary structures can exist becomes narrower in the presence of the polarization interaction. In both limits there exists a critical value of grain size beyond which the DASW cannot propagate.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Over the last two decades, there has been a great deal of interest in understanding the propagation characteristics of linear and nonlinear waves in complex plasmas, in the laboratory environment as well as in space and astrophysical objects. The dust acoustic solitary wave (DASW) is one of the nonlinear waves which retains its shape over a long distance during its propagation. The polarization force which arises from any kind of deformation of the Debye sheath around the particles in the background of nonuniform plasmas can lead to significant changes in the propagation characteristics of linear and nonlinear waves.
Main results. In this paper, we study—theoretically, using two different approaches—the modification arising in the propagation characteristics of DASW due to the presence of polarization force acting on the dust grains in an inhomogeneous plasma. In the small amplitude limit, we find that with an increase of polarization force, the amplitude of a solitary wave increases, whereas the width decreases for a given Mach number. For an arbitrary amplitude limit, we find a similar effect for the amplitude and the width of the solitary pulse. In addition, we find that the range of Mach numbers where solitary structures can exist becomes narrower in the presence of the polarization interaction. In both limits, there exists a critical value of grain size beyond which the dust acoustic solitary wave cannot propagate.
Wider implications. Experimental verification of this prediction is desireable, but perhaps this would be only possible in experiments under microgravity conditions, as large grains (≥ 10μm) have to be used.
Figure. Time evolution of the potential profiles of a solitary wave in the absence (red line) and presence (blue line) of polarization force for a given Mach number and plasma parameters. Every normalized potential profile has been given a shift of 
= −0.072 with respect to the previous one to avoid overlapping. The amplitude of the solitary structure is seen to increase and its width to decrease in presence of polarization interaction.