We present experiments performed in a recirculating fiber loop in which we realize the single-shot observation of the space and time interaction of two and three bright solitons. The space–time evolutions observed in experiments provide clear evidence of a nearly-integrable nonlinear wave dynamics that can be easily interpreted within the framework of the inverse scattering transform (IST) method. In particular collisions between solitons are found to be almost perfectly elastic in the sense that they occur without velocity change and with only a position (time) shift quantitatively well described by numerical simulations of the integrable nonlinear Schrödinger equation. Additionally our experiments provide the evidence that the position (time) shifts arising from the interaction among three solitons are determined by elementary pairwise interactions, as it is well known in the IST theory.