Linear stability of elastic 2-line solitons for the KP-II equation

TL;DR

This paper investigates the linear stability of elastic 2-line solitons in the KP-II equation, revealing how their interactions can be modeled by a damped wave equation describing phase shifts.

Contribution

It introduces a novel analysis of 2-line soliton stability using Darboux transformations and models their interactions with a damped wave equation.

Findings

2-line solitons interact elastically

Resonant eigenfunctions evolve via a damped wave equation

Provides insights into phase shift dynamics in soliton interactions

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.