  The Koutras-McIntosh family of metrics include conformally flat pp-waves and
the Wils metric. It appeared in a paper of 1996 by Koutras-McIntosh as an
example of a pure radiation spacetime without scalar curvature invariants or
infinitesimal symmetries. Here we demonstrate that these metrics have no
"hidden symmetries", by which we mean Killing tensors of low degrees. For the
particular case of Wils metrics we show the nonexistence of Killing tensors up
to degree 6.
  The technique we use is the geometric theory of overdetermined PDEs and the
Cartan prolongation-projection method. Application of those allows to prove the
nonexistence of polynomial in momenta integrals for the equation of geodesics
in a mathematical rigorous way. Using the same technique we can completely
classify all lower degree Killing tensors and, in particular, prove that for
generic pp-waves all Killing tensors of degree 3 and 4 are reducible.
