  In this paper, we mainly present some new solutions of the Hom-Yang-Baxter
equation from Hom-algebras,
  Hom-coalgebras and Hom-Lie algebras, respectively.
  Also, we prove that these solutions are all self-inverse and give some
examples.
  Finally, we introduce the notion of Hom-Yang-Baxter systems and obtain two
kinds of Hom-Yang-Baxter systems.
