We consider the quadratic and cubic KP-I and NLS models in 1 + 2 dimensions with periodic boundary conditions. We show that the spatially periodic traveling waves (with period K) in the form u(t,x,y) = φ(x-ct) are spectrally and linearly unstable when the perturbations are taken to be with the same period. This strong instability implies other instabilities considered recently-for example, with respect to perturbations with periods nK, n = 2, 3,... or bounded perturbations.
