  Recently, Hirayama and Yamashita have presented an ansatz that allows us to
construct a class of solutions for the SU(2) Skyrme model. Though these
solutions are not solitonic, they provide us with an example on how the plane
wave solutions arise in nonlinear field theories. In this paper, we investigate
the applicability of the ansatz for the SU(3) Skyrme model. We explicitly
construct a class of solutions for the SU(3) model, which in the simplest
circumstance is reduced to a combination of the plane waves and Weierstrass
elliptic functions. We also discuss some properties of these solutions. For
example, the intrinsic structure of these solutions is found to describe an
asymmetrical top rotating in the complex three-dimensional space.
