  We study transverse stability and instability of one-dimensional
small-amplitude periodic traveling waves of a generalized
Kadomtsev-Petviashvili equation with respect to two-dimensional perturbations,
which are either periodic or square-integrable in the direction of the
propagation of the underlying one-dimensional wave and periodic in the
transverse direction. We obtain transverse instability results in KP-fKdV,
KP-ILW, and KP-Whitham equations. Moreover, assuming the spectral stability of
one-dimensional wave with respect to one-dimensional square-integrable periodic
perturbations, we obtain transverse stability results in aforementioned
equations.
