  In this paper we consider the nonlinear dispersive wave equation on the real
line,
$u_t-u_{txx}+[f(u)]_x-[f(u)]_{xxx}+\bigl[g(u)+\frac{f''(u)}{2}u_x^2\bigr]_x=0$,
that for appropriate choices of the functions $f$ and $g$ includes well known
models, such as Dai's equation for the study of vibrations inside elastic rods
or the Camassa--Holm equation modelling water wave propagation in shallow
water. We establish a local-in-space blowup criterion (i.e., a criterion
involving only the properties of the data $u_0$ in a neighbourhood of a single
point) simplifying and extending earlier blowup criteria for this equation. Our
arguments apply both to the finite and infinite energy case, yielding the
finite time blowup of strong solutions with possibly different behavior as
$x\to+\infty$ and $x\to-\infty$.
