  We study the transverse spectral stability of the one-dimensional
small-amplitude periodic traveling wave solutions of the (2+1)-dimensional
Konopelchenko-Dubrovsky (KD) equation. We show that these waves are
transversely unstable with respect to two-dimensional perturbations that are
periodic in both directions with long wavelength in the transverse direction.
We also show that these waves are transversely stable with respect to
perturbations which are either mean-zero periodic or square-integrable in the
direction of the propagation of the wave and periodic in the transverse
direction with finite or short wavelength. We discuss the implications of these
results for special cases of the KD equation - namely, KP-II and mKP-II
equations.
