  We present and analyze a new non-perturbative radiative solution of Horndeski
gravity. This exact solution is constructed by a disformal mapping of a seed
solution of the shift-symmetric Einstein-Scalar system belonging to the
Robinson-Trautman geometry describing the gravitational radiation emitted by a
time-dependent scalar monopole. After analyzing in detail the properties of the
seed, we show that while the general relativity solution allows for shear-free
parallel transported null frames, the disformed solution can only admit
parallel transported null frames with a non-vanishing shear. This result shows
that, at the nonlinear level, the scalar-tensor mixing descending from the
higher-order terms in Horndeski dynamics can generate shear out of a pure
scalar monopole. We further confirm this analysis by identifying the spin-0 and
spin-2 polarizations in the disformed solution using the Penrose limit of our
radiative solution. Finally, we compute the geodesic motion and the memory
effects experienced by two null test particles with vanishing initial relative
velocity after the passage of the pulse. This exact radiative solution offers a
simple framework to witness nonlinear consequences of the scalar-tensor mixing
in higher-order scalar-tensor theories.
