  In this article we study global existence and blow-up of solutions for a
general class of nonlocal nonlinear wave equations with power-type
nonlinearities, $u_{tt}-Lu_{xx}=B(- |u|^{p-1}u)_{xx}, ~(p>1)$, where the
nonlocality enters through two pseudo-differential operators $L$ and $B$. We
establish thresholds for global existence versus blow-up using the potential
well method which relies essentially on the ideas suggested by Payne and
Sattinger. Our results improve the global existence and blow-up results given
in the literature for the present class of nonlocal nonlinear wave equations
and cover those given for many well-known nonlinear dispersive wave equations
such as the so-called double-dispersion equation and the traditional
Boussinesq-type equations, as special cases.
