A Dimension-Breaking Phenomenon for Water Waves with Weak Surface Tension
Författare
Summary, in English
It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schrödinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.
Avdelning/ar
- Matematik (naturvetenskapliga fakulteten)
- Partial differential equations
Publiceringsår
2016-05-01
Språk
Engelska
Sidor
747-807
Publikation/Tidskrift/Serie
Archive for Rational Mechanics and Analysis
Volym
220
Issue
2
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Springer
Ämne
- Fluid Mechanics and Acoustics
- Mathematical Analysis
Status
Published
Projekt
- Nonlinear Water Waves
Forskningsgrupp
- Partial differential equations
ISBN/ISSN/Övrigt
- ISSN: 0003-9527