Transverse spectral instability in generalized Kadomtsev-Petviashvili equation
Analysis of PDEs
2022-04-01 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2109.00370,
title = {Transverse spectral instability in generalized Kadomtsev-Petviashvili equation},
author = {Bhavna and Atul Kumar and Ashish Kumar Pandey},
journal= {arXiv preprint arXiv:2109.00370},
year = {2022}
}