  In a recent paper, Struwe considered the Cauchy problem for a class of
nonlinear wave and Scr\"odinger equations.
  Under some assumptions on the nonlinearities, it was shown that uniqueness of
classical solutions can be obtained in the much larger class of distribution
solutions satisfying the energy inequality. As pointed out in [38], the
conditions on the nonlinearities are satisfied for any polynomial growth but
they fail to hold for higher growth (for example ${\rm e}^{u^2}$).
  Our aim here is to improve Struwe's result by showing that uniqueness holds
for more general nonlinearities including higher growth or oscillations.
