This paper investigates the interaction of two dust acoustic solitons in a dusty plasma by considering the influence of the Cairns–Gurevich polarization force. Modified Korteweg–de Vries (mKdV) equations are derived using the modified Poincaré–Lighthill–Kuo method, and the phase shifts in the solitons' trajectories after the interaction are examined. The study reveals that the derived nonlinear equations are influenced by various plasma parameters, including the polarization parameter (R), dust-to-ion temperature ratio (σd), and the number of nonthermal ion parameters (α). Numerical results demonstrate that only rarefactive electrostatic nonlinear waves can propagate in this system within the range of relevant parameters of the experiment. While the findings align with previous research in terms of phase speed and soliton behavior, this study identifies a new dependency of phase shifts on the amplitudes of the colliding waves, which distinguishes it from earlier works. This study is expected to enhance our understanding of nonlinear localized structures in dusty plasmas with nonthermal trapped ions.
