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Solitary Wave Solutions to a Class of Modified Green–Naghdi Systems

Duchêne, Vincent; Nilsson, Dag LU and Wahlén, Erik LU (2018) In Journal of Mathematical Fluid Mechanics 20(3). p.1059-1091
Abstract

We provide the existence and asymptotic description of solitary wave solutions to a class of modified Green–Naghdi systems, modeling the propagation of long surface or internal waves. This class was recently proposed by Duchêne et al. (Stud Appl Math 137:356–415, 2016) in order to improve the frequency dispersion of the original Green–Naghdi system while maintaining the same precision. The solitary waves are constructed from the solutions of a constrained minimization problem. The main difficulties stem from the fact that the functional at stake involves low order non-local operators, intertwining multiplications and convolutions through Fourier multipliers.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Fluid Mechanics
volume
20
issue
3
pages
33 pages
publisher
Birkhaüser
external identifiers
  • scopus:85051423858
ISSN
1422-6928
DOI
10.1007/s00021-017-0355-0
language
English
LU publication?
yes
id
836f83ca-cdec-4fc5-bce1-6b8cce989523
date added to LUP
2018-09-07 12:05:34
date last changed
2019-01-06 14:03:50
@article{836f83ca-cdec-4fc5-bce1-6b8cce989523,
  abstract     = {<p>We provide the existence and asymptotic description of solitary wave solutions to a class of modified Green–Naghdi systems, modeling the propagation of long surface or internal waves. This class was recently proposed by Duchêne et al. (Stud Appl Math 137:356–415, 2016) in order to improve the frequency dispersion of the original Green–Naghdi system while maintaining the same precision. The solitary waves are constructed from the solutions of a constrained minimization problem. The main difficulties stem from the fact that the functional at stake involves low order non-local operators, intertwining multiplications and convolutions through Fourier multipliers.</p>},
  author       = {Duchêne, Vincent and Nilsson, Dag and Wahlén, Erik},
  issn         = {1422-6928},
  language     = {eng},
  month        = {09},
  number       = {3},
  pages        = {1059--1091},
  publisher    = {Birkhaüser},
  series       = {Journal of Mathematical Fluid Mechanics},
  title        = {Solitary Wave Solutions to a Class of Modified Green–Naghdi Systems},
  url          = {http://dx.doi.org/10.1007/s00021-017-0355-0},
  volume       = {20},
  year         = {2018},
}