Overlapping soliton during the concentric interaction of cylindrical dark solitons in a bounded dusty plasma with dust charge variation

The combined effect of the cylindrical boundary and the adiabatic variation in dust charges on the spatiotemporal evolution of the overlapping soliton in a dusty plasma is studied in detail. We derive the mathematical expression of the overlapping soliton and investigate the effect of dust charging and the influence of its adiabatic variation on the evolution process of the soliton structure. Numerical results indicate that the basic properties of the merged pulse are partially similar to the recent experimental results reported for the interaction of planar solitons in strongly coupled dusty plasmas by Harvey et al., Phys. Rev. E 81, 057401 (2010) and Sharma et al. Phys. Rev. E 89, 013110 (2014). Moreover, it is found that the soliton amplitude and the occurrence time of its peak value increase with the increase in Rn and RT, and the increasing rate of the peak amplitude decreases with the increase in Rn and increases with the increase in RT. As time t increases, the overlapping soliton moves to the inside-traveling direction (i.e., r → 0); before reaching the peak amplitude, the merged pulse gradually increases its amplitude and decreases its width and traveling velocity; after reaching the peak amplitude, the soliton gradually decreases its amplitude and increases its width and velocity. It is also noted that when dust charge variation is considered, solitons with bigger values of Rn (or RT) experience longer phase delays. Comparatively speaking, Rn has a more remarkable effect on the physical properties of the overlapping soliton.