LAUSR

In order to investigate the propagation characteristics of linear and non‐linear ion acoustic waves (IAWs) in electron–positron–ion quantum plasma in the presence of external weak magnetic field, we have used a quantum hydrodynamic model, and degenerate statistics for the electrons and positrons are taken into account. It is found that the linear dispersion relation of the IAW was modified by the externally applied magnetic field. By using the reductive perturbation technique, a gyration‐modified Korteweg‐de Vries equation is derived for finite amplitude non‐linear IAWs. Time‐dependent numerical simulation shows the formation of an oscillating tail in front of the ion acoustic solitons in the presence of a weak magnetic field. It is also seen that the amplitude and width of solitons and oscillating tails are affected by the relevant plasma parameters such as quantum diffraction, positron concentration, and magnetic field. We have performed our analysis by extending it to account for approximate soliton solution by asymptotic perturbation technique and non‐linear analysis via a dynamical system approach. The analytical results show the distortion of the shape of the localized soliton with time, and the non‐linear analysis confirms the generation of oscillating tails.