Linear stability of elastic 2-line solitons for the KP-II equation
Analysis of PDEs
2023-07-20 v1 Mathematical Physics
math.MP
Abstract
The KP-II equation was derived by Kadomtsev and Petviashvili to explain stability of line solitary waves of shallow water. Using the Darboux transformations, we study linear stability of 2-line solitons whose line solitons interact elastically each other. Time evolution of resonant continuous eigenfunctions is described by a damped wave equation in the transverse variable which is supposed to be a linear approximation of the local phase shifts of modulating line solitons.
Keywords
Cite
@article{arxiv.2307.09932,
title = {Linear stability of elastic 2-line solitons for the KP-II equation},
author = {Tetsu Mizumachi},
journal= {arXiv preprint arXiv:2307.09932},
year = {2023}
}
Comments
To appear in Quarterly of Applied Mathematics