"In the absence of others" means considering the effect of each individual wave as if it is acting alone, without the influence or presence of the other waves. In the given context, it explains that the resultant displacement of a particle is calculated by adding the displacements caused by each wave separately. This principle is known as the superposition of waves. So, "in the absence of others" helps to clarify that each wave's effect is treated independently before summing them algebraically.