Transverse spectral instability in generalized Kadomtsev-Petviashvili equation

TL;DR

This paper investigates the transverse spectral stability and instability of small-amplitude periodic traveling waves in generalized Kadomtsev-Petviashvili equations, providing new insights into their stability behavior under various perturbations.

Contribution

It offers novel transverse stability and instability results for generalized KP equations, including KP-fKdV, KP-ILW, and KP-Whitham, under different perturbation conditions.

Findings

Transverse instability results for KP-fKdV, KP-ILW, and KP-Whitham equations.

Transverse stability established assuming spectral stability of one-dimensional waves.

Analysis covers both periodic and square-integrable perturbations.

Abstract

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.