Vortex rings are a special soliton wave that are known to carry matter over a distance as well as energy. This can easily be demonstrated using a cardboard 'vortex canon' filled with smoke. The smoke makes the vortex rings visible as they are fired out of the canon.
But to my question - are there any other types of waves that are also known to carry matter?
Most traveling waves that travel through media leave the media and any matter behind as the energy propagates forward.