Several theoretical works have shown that solitons -- waves that self-maintain constant shape and velocity as they propagate -- can be used as a physical computational reservoir, a concept where machine learning algorithms designed for digital computers are replaced by analog physical systems that exhibit nonlinear dynamical behaviour. Here we propose and experimentally validate a novel reservoir computing (RC) system that for the first time employs solitary-like (SL) waves propagating on the surface of a liquid film flowing over an inclined surface. We demonstrate the ability of the SL wave RC system (SLRC) to forecast chaotic time series and to successfully pass essential benchmark tests, including a memory capacity test and a Mackey-Glass model test.