Asymptotic linear stability of Benney-Luke line solitary waves in 2D

In this paper, we study transverse linear stability of line solitary waves to the two-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in 3D. In the case where the surface tension is weak or negligible, we find a curve of resonant continuous eigenvalues...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2017-08, Vol.30 (9), p.3419-3465
Main Authors: Mizumachi, Tetsu, Shimabukuro, Yusuke
Format: Article
Language:English
Subjects:
line solitary wave
long wave models
transverse linear stability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study transverse linear stability of line solitary waves to the two-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in 3D. In the case where the surface tension is weak or negligible, we find a curve of resonant continuous eigenvalues of the linearized operator in a neighborhood of λ=0. Time evolution of these resonant continuous eigenmodes is described by a 1D damped wave equation in the transverse variable and it gives a linear approximation of the local phase shifts of modulating line solitary waves. In exponentially weighted space whose weight function increases in the direction of the motion of the line solitary wave, the other part of solutions to the linearized equation decays exponentially as t→∞.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa7cc7