•The nonlinear propagation of soliton waves can be expressed by different equations.•KdV equation includes the equilibrium between nonlinearity and dispersion sentences, which gives information about the soliton waves.•One of the distribution functions that have been utilized in the last few years is the C-T distribution function.•The results demonstrated that the parameters α and q have a great impact on phase. Velocity, nonlinear and dispersive coefficients, Sagdeev potential, maximum amplitude, and width of IASWs. The interaction of positron acoustic soliton waves (PASWs) with the arbitrary collision angle in plasma including cold fluid positrons, stationary ions and electrons with Kappa-Cairns (K-C) distribution function have been studied. The equations of Korteweg-de Vries (KdV) and the phase shifts are obtained by employing the extended Poincaré–Lighthill–Kuo (PLK) method for the two colliding waves. The influences of parameters of the K-C distribution function (κ and α), the collision angle θ and the proportion of the ion (electron) and positron unperturbed densities (βi(βe)) on the phase shifts are investigated.