Transverse spectral instability in generalized Kadomtsev-Petviashvili equation

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

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