Nonlinear dynamics of soliton collisions in electronegative plasmas: The phase shifts of the planar KdV- and mkdV-soliton collisions

The collisions of weakly nonlinear structures in an electronegative plasma consisting of Boltzmann electrons, Boltzmann negative ions, and cold mobile positive ions are investigated depending on experimental data. Our attention is focused on the study of the face-to-face soliton collisions, i.e. head-on soliton collisions. To do this, the extended Poincaré–Lighthill–Kuo (PLK) reductive perturbation method is used. The present study is split into two parts: the first one, called generic case. In this case, the two-coupled Korteweg–de Vries (KdV) equations and the analytical phase shifts after the head-on collision of the two-KdV solitons are obtained. Our numerical calculations, showed that both compressive and rarefactive solitons can exist in such plasma, depending on the relevant physical plasma parameters, namely the electrons-to-negative ion temperature ratio and the negative ion concentration. It is found that the phase shift has a positive sign for compressive solitary structures and negative sign for rarefactive solitary structures. At the critical value of the temperature ratio, the two-coupled modified Kortwege–de Vries (mKdV) equations are used to study the soliton collision rather than the two-KdV equations and the analytical phase shifts after the collision are derived. In the latter case (called special case), the combinations of negative and positive soliton collision can occur, contrary to the generic case, where both soliton collisions necessarily have the same polarity. The plasma parameter values for laboratory experiment are taken for discussion.