Transverse spectral instability in generalized Kadomtsev–Petviashvili equation

Abstract

We study transverse stability and instability of one-dimensional small-amplitude periodic travelling 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 the aforementioned equations.