  We numerically investigate transverse stability and instability of so-called
cnoidal waves, i.e., periodic traveling wave solutions of the Korteweg-de Vries
equation, under the time-evolution of the Kadomtsev-Petviashvili equation. In
particular, we find that in KP-I small amplitude cnoidal waves are stable (at
least for spatially localized perturbations) and only become unstable above a
certain threshold. In contrast to that, KP-II is found to be stable for all
amplitudes, or, equivalently, wave speeds. This is in accordance with recent
analytical results for solitary waves given in \cite{RT1, RT2}.
