The dynamics of the nonlinear ion acoustic waves are investigated in the presence of an external weak magnetic field in pair-ion plasma in which the mass (temperature) of the positive ions are smaller (larger) than that of the negative ions. The linear dispersion relation of the ion acoustic wave is found to be modified by the externally applied magnetic field. The standard perturbative approach leads to a modified form of Korteweg-de Vries equation. The analytical as well as numerical solutions reveal that the localized (solitary wave) solutions decay slowly algebraically due to the Lorentz force by radiating energy to the tails of the dispersive ion acoustic waves. The results are discussed in the context of the lower region of D-layer ionospheric plasma. © 2015 The Royal Swedish Academy of Sciences.