We report an experimental observation of rotating depression soliton sets on the inner surface of a viscous liquid ring, carrying background waves. These occur within a rotating shallow layer of oil inside a stationary cylindrical container. The solitons are organized either in single, two, or regular polygonal (triangle and hexagon) clusters; they travel in unison at a higher speed than the background traveling waves. The spectral power density reveals a possible energy exchange between the soliton clusters and the background mixed radial-azimuthal modulations through wave radiation.