The solitary periodic soliton and formation of shock with phase shift in multi-component unmagnetized dusty plasmas

Abstract A multi-component unmagnetized dusty plasma, comprising negatively charged heavy ions at two different temperatures, q-nonextensive distributed electrons, Cairn’s distributed nonthermal ions, and arbitrarily charged mobile dust, is considered to study the head-on collision (HOC) phenomena of dust-acoustic (DA) waves (DAWs), and dust-acoustic shock waves (DASHWs) and the formation of DA Korteweg de Vries (KdV) and KdV Burger (KdVB) solitons, solitonic and periodic soliton structures, higher-order DA solitons’ (DASs) structure, as well as Sagdeev potential structure. The extended Poincaré-Lighthill-Kuo (ePLK) method is used to derive the KdV and KdVB equations describing the dynamics of solitons and shocks in plasmas. It is found that the relevant plasma parameters are vital in forming the soliton structures, phase shifts, and the collision processes of KdV and KdVB solitons. The compressive solitonic potential structures are produced due to the effects of the temperature ratio of low-temperature ion to high-temperature ion ( σ 1 ) and the strength of electron nonextensivity ( q ). On the other hand, due to the effect of σ 1 , both compressive and rarefactive periodic potentials are produced. The superposition principle is followed by the solitons, but not by the shocks in the colliding regions. For the higher-order correction, both the compressive and rarefactive DASs are produced, whereas, in the zeroth-order case, only the compressive DASs are produced. Both the depth and width of the Sagdeev potential of DAWs increase due to the influence of the density ratio of the lower ion to dust ( μ 1 ) and q but decrease with increasing nonthermality parameter ( β ).