  We prove that the theorem of Mouhot and Villani on Landau damping near
equilibrium for the Vlasov-Poisson equations on $\mathbb{T}_x \times
\mathbb{R}_v$ cannot, in general, be extended to high Sobolev spaces in the
case of gravitational interactions. This is done by showing in every Sobolev
space, there exists background distributions such that one can construct
arbitrarily small perturbations that exhibit arbitrarily many isolated
nonlinear oscillations in the density. These oscillations are known as plasma
echoes in the physics community. For the case of electrostatic interactions, we
demonstrate a sequence of small background distributions and asymptotically
smaller perturbations in $H^s$ which display similar nonlinear echoes. This
shows that in the electrostatic case, any extension of Mouhot and Villani's
theorem to Sobolev spaces would have to depend crucially on some additional
non-resonance effect coming from the background -- unlike the case of
Gevrey-$\nu$ with $\nu < 3$ regularity, for which results are uniform in the
size of small backgrounds. In particular, the uniform dependence on small
background distributions obtained in Mouhot and Villani's theorem in Gevrey
class is false in Sobolev spaces.
