  We develop a variational theory for a dipolar condensate in an elongated
(cigar shaped) confinement potential. Our formulation provides an effective
one-dimensional extended meanfield theory for the ground state and its
collective excitations. We apply our theory to investigate the properties of
rotons in the system comparing the variational treatment to a full numerical
solution. We consider the effect of quantum fluctuations on the scattering
length at which the roton excitation softens to zero energy.
