  We consider nonminimally coupled scalar fields to explore the Siklos
spacetimes in three dimensions. Their interpretation as exact gravitational
waves propagating on AdS restrict the source to behave as a pure radiation
field. We show that the related pure radiation constraints single out a unique
self-interaction potential depending on one coupling constant. For a vanishing
coupling constant, this potential reduces to a mass term with a mass fixed in
terms of the nonminimal coupling parameter. This mass dependence allows the
existence of several free cases including massless and tachyonic sources. There
even exists a particular value of the nonminimal coupling parameter for which
the corresponding mass exactly compensates the contribution generated by the
negative scalar curvature, producing a genuinely massless field in this curved
background. The self-interacting case is studied in detail for the conformal
coupling. The resulting gravitational wave is formed by the superposition of
the free and the self-interaction contributions, except for a critical value of
the coupling constant where a non-perturbative effect relating the strong and
weak regimes of the source appears. We establish a correspondence between the
scalar source supporting an AdS wave and a pp wave by showing that their
respective pure radiation constraints are conformally related, while their
involved backgrounds are not. Finally, we consider the AdS waves for
topologically massive gravity and its limit to conformal gravity.
