  Presented are exactly integrable models with pure radiation in R^2 gravity
with a cosmological constant, related to wave-like Shapovalov spacetimes type
II. Spatially homogeneous models of Shapovalov spaces were considered. The
obtained solutions belong to spaces of type III according to the Bianchi
classification. For the models under consideration, exact solutions of the
equations of motion of test particles are obtained in the Hamilton-Jacobi
formalism.
