Numerical modelling of overtaking collisions of dust acoustic waves in plasmas

The overtaking collision between two single and unidirectional dust acoustic waves in dusty plasmas consisting of Boltzmann electrons and ions, and negative dust grains has been investigated by PIC simulation method. The well-known physical phenomenon is that the larger soliton moves faster, approaches the smaller one and after the overtaking collision both resume their original shape and speed with different phase shifts. The merging amplitude of two solitons and phase shifts of solitons after collision are given. These PIC results are compared with the overtaking collision of two-soliton solution (TSS) of KdV equaiton obtained by Hirota bilinear method. Comparisons between two indicates that if the amplitude of fast soliton is large enough or the amplitude of slow soliton is small enough, the simulation results are consistent with the interaction of Hirota results.