In the article Creation and annihilation of mobile fractional solitons in atomic chains the authors claim that they prepared 1D solitons which can be used in topological quantum computing. Based on the abstract and introduction, it seems to me that features the solitons show are those of anyons.
I know that soliton is more broader term for self propagating wave package, i.e. the wave preserves amplitude, energy and shape. Solitons can appear in a mechanical medium as well as in form of EM waves.
Therefore, I am a little bit confused by terminology. What type of quassiparticle the solitons are in this case. Are they special type of anyons? Or are anyons special type of solitons?