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Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations

Groves, Mark D.; Sun, Shu Ming and Wahlén, Erik LU (2016) In Comptes Rendus Mathématique 354(5). p.486-492
Abstract

We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Comptes Rendus Mathématique
volume
354
issue
5
pages
7 pages
publisher
Editions scientifiques Elsevier
external identifiers
  • Scopus:84961773634
ISSN
1631-073X
DOI
10.1016/j.crma.2016.02.005
language
English
LU publication?
yes
id
917b1b5e-a9e4-423b-90f7-9f8f0b1cd3b9
date added to LUP
2016-05-10 13:21:19
date last changed
2016-11-21 09:55:56
@misc{917b1b5e-a9e4-423b-90f7-9f8f0b1cd3b9,
  abstract     = {<p>We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.</p>},
  author       = {Groves, Mark D. and Sun, Shu Ming and Wahlén, Erik},
  issn         = {1631-073X},
  language     = {eng},
  month        = {05},
  number       = {5},
  pages        = {486--492},
  publisher    = {ARRAY(0x8c160b0)},
  series       = {Comptes Rendus Mathématique},
  title        = {Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations},
  url          = {http://dx.doi.org/10.1016/j.crma.2016.02.005},
  volume       = {354},
  year         = {2016},
}