The collision between two solitary waves in a one-dimensional Lennard-Jones chain of identical masses with nearest-neighbour interaction has been studied numerically. The authors consider two solitary waves of high energy travelling in the same direction such that they approach each other and collide. After collision there emerge again two solitary waves. A (small) disturbance, however, stays behind and the energy and momenta of the outcoming solitary waves are not equal to the corresponding quantities of the incoming ones. The effects are relatively small, however. Calculations are performed for different ratios of the velocity of the faster solitary wave to the velocity of the slower one. The effects mentioned above ultimately diminish if this ratio tends to unity. Further they calculate the influence of shifting the initial position of one of the solitons for fixed initial position of the other one. The results are interpreted in terms of the individual motion of the particles.