Classifications of surface waves in magneto-electro-elastic materials

•The classifications of surface waves in magneto-electro-elastic materials, which is rarely studied, is carried out.•The number of distinct eigenvalues and the number of independent eigenvectors of the matrix N(v) play an important role in determining the surface wave solutions.•The simple and semisimple properties, as well as ten types of degenerate cases of the real matrix N(v), are considered.•A total of fifteen distinct types of surface waves is identified.