  We study the stability of a quasi-one-dimensional dipolar Bose-Einstein
condensate (dBEC) that is perturbed by a weak lattice potential along its axis.
Our numerical simulations demonstrate that systems exhibiting a roton-maxon
structure destabilize readily when the lattice wavelength equals either half
the roton wavelength or a low roton subharmonic. We apply perturbation theory
to the Gross-Pitaevskii and Bogoliubov de Gennes equations to illustrate the
mechanisms behind the instability threshold. The features of our stability
diagram may be used as a direct measurement of the roton wavelength for
quasi-one-dimensional geometries.
