  Scaling similarity solutions of three integrable PDEs, namely the
Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered.
It is shown that the resulting ODEs may be written as non-autonomous
Hamiltonian equations, which are time-dependent generalizations of the
well-known integrable H\'{e}non-Heiles systems. The (time-dependent)
Hamiltonians are given by logarithmic derivatives of the tau-functions
(inherited from the original PDEs). The ODEs for the similarity solutions also
have inherited B\"{a}cklund transformations, which may be used to generate
sequences of rational solutions as well as other special solutions related to
the first Painlev\'{e} transcendent.
