The solitons collision (head-on collision) and rogue waves in an unmagnetized plasma comprising nonthermal-nonextensive distributed (Cairns-Tsallis) electrons and cold ions are investigated. For solitons collision, the extended Poincaré–Lighthill–Kuo (PLK) method is employed to derive the coupled Korteweg-de Vries (KdV) equations and their corresponding phase shifts. It is found that solitons having two polarities can propagate in the present model. The coefficients of the nonlinear terms of the coupled KdV equations vanish at a critical value of nonthermality. Therefore, another set of coupled modified KdV (mKdV) equations with cubic nonlinearity is derived and the corresponding phase shifts are calculated. It is found analytically and numerically that the solutions of the coupled KdV equations allow solitons collision only when the solitons have the same polarity, whereas the coupled mKdV equations allow the collisions between the two solitons of the same and opposite polarities. The influence of the nonthermal-nonextensive parameters on the phase shifts of the solitons collision is examined. Furthermore, the rogue waves are studied in the framework of the mKdV equation. The behavior of the rogue waves is analyzed using the nonlinear Schrödinger equation (NLSE), derived from the mKdV equation. It is found that the rogue wave amplitude shrinks with the increase of the nonextensive parameter. The NLSE derived from the KdV equation cannot support the presence of rogue waves.
General formulation for electrostatic solitons in multicomponent nonthermal plasmas