A numerical investigation of the evolution of localized disturbances in the form of solitary waves is performed for the full system of equations describing planar waves in a cold collisionless quasineutral plasma. It is shown that, for a wide range of angles of inclination of the magnetic field vector to the direction of wave propagation, such a kind of initial disturbance never results in a wave propagating steadily, but leads to decay due to radiation of periodic waves. These results confirm the recent theoretical conclusion of Il'ichev [J. Plasma Phys.55, 181–194 (1996)] about the non-existence of solitary waves in a cold plasma for the range of angles of inclination in question.