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Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

Haragus, Mariana and Wahlén, Erik LU (2017) In Journal of Differential Equations 262(4). p.3235-3249
Abstract

We consider a fifth-order Kadomtsev–Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Dispersive equations, Generalized solitary waves, Periodic waves, Transverse stability
in
Journal of Differential Equations
volume
262
issue
4
pages
15 pages
publisher
Elsevier
external identifiers
  • scopus:85006298129
  • wos:000392904200005
ISSN
0022-0396
DOI
10.1016/j.jde.2016.11.025
language
English
LU publication?
yes
id
ad15c2f3-838b-4b31-86e5-cffa1aa1e0a3
date added to LUP
2017-02-03 10:15:08
date last changed
2018-01-07 11:47:58
@article{ad15c2f3-838b-4b31-86e5-cffa1aa1e0a3,
  abstract     = {<p>We consider a fifth-order Kadomtsev–Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.</p>},
  author       = {Haragus, Mariana and Wahlén, Erik},
  issn         = {0022-0396},
  keyword      = {Dispersive equations,Generalized solitary waves,Periodic waves,Transverse stability},
  language     = {eng},
  month        = {02},
  number       = {4},
  pages        = {3235--3249},
  publisher    = {Elsevier},
  series       = {Journal of Differential Equations},
  title        = {Transverse instability of periodic and generalized solitary waves for a fifth-order KP model},
  url          = {http://dx.doi.org/10.1016/j.jde.2016.11.025},
  volume       = {262},
  year         = {2017},
}