Transverse instability of periodic and generalized solitary waves for a fifth-order KP model
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/ad15c2f3-838b-4b31-86e5-cffa1aa1e0a3
- author
- Haragus, Mariana and Wahlén, Erik LU
- organization
- publishing date
- 2017-02-15
- 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
- project
- Nonlinear Water Waves
- language
- English
- LU publication?
- yes
- id
- ad15c2f3-838b-4b31-86e5-cffa1aa1e0a3
- date added to LUP
- 2017-02-03 10:15:08
- date last changed
- 2024-06-24 13:42:18
@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}},
keywords = {{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}},
doi = {{10.1016/j.jde.2016.11.025}},
volume = {{262}},
year = {{2017}},
}