  We prove unique continuation properties of solutions to a large class of
nonlinear, non-local dispersive equations. The goal is to show that if
$u_1,\,u_2$ are two suitable solutions of the equation defined in $\mathbb
R^n\times[0,T]$ such that for some non-empty open set $\Omega\subset \mathbb
R^n\times[0,T]$, $u_1(x,t)=u_2(x,t)$ for $(x,t) \in \Omega$, then
$u_1(x,t)=u_2(x,t)$ for any $(x,t)\in\mathbb R^n\times[0,T]$. The proof is
based on static arguments. More precisely, the main ingredient in the proofs
will be the unique continuation properties for fractional powers of the
Laplacian established by Ghosh, Salo and Ulhmann in \cite{GhSaUh}, and some
extensions obtained here.
