Effects of Polarized Debye Sheath and Trapped Ions on Solitary Structures in a Strongly Coupled Inhomogeneous Dusty Plasma

The effects of polarized Debye sheath (i.e., polarization force) and trapped ions on the nonlinear propagation of dust-acoustic (DA) waves are investigated, including the dust inhomogeneity in the strongly coupled dusty plasma. Dispersion relation and propagation of possible modes are calculated from the underlying usual hydrodynamic model. Then, a variable coefficient's modified Korteweg-de Vries equation describing the dynamics of DA solitary waves is derived from a weakly nonlinear analysis, and is solved to get the stationary solutions using a sine-cosine method. It is found that for experimental conditions under which the interaction of resonant ions and highly negatively charged dust grains is important, only soliton with negative potential can propagate in such a strongly coupled inhomogeneous dusty plasma. In the presence of trapped ions, the amplitude of solitary waves is found to be smaller compared with that for the Boltzmann distribution. Moreover, it is argued that the soliton profile is highly sensitive to the effects of modified strength of the polarization force, dust temperature, and dust density inhomogeneity.