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BOUSSINESQ'S EQUATION FOR WATER WAVES : ASYMPTOTICS IN SECTOR V

Charlier, C. LU and Lenells, J. LU (2024) In SIAM Journal on Mathematical Analysis 56(3). p.4104-4142
Abstract

We consider the Boussinesq equation on the line for a broad class of Schwartz initial data for which (i) no solitons are present, (ii) the spectral functions have generic behavior near \pm1, and (iii) the solution exists globally. In a recent work, we identified 10 main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term. In this paper, we give a proof for the formula corresponding to the sector xt \in(0, \surd13).

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Boussinesq equation, long-time asymptotics, Riemann-Hilbert problem
in
SIAM Journal on Mathematical Analysis
volume
56
issue
3
pages
39 pages
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • scopus:85190821361
ISSN
0036-1410
DOI
10.1137/23M1587671
language
English
LU publication?
yes
id
95485309-8640-43aa-a81b-4b278d5efafd
date added to LUP
2025-01-14 14:43:03
date last changed
2025-04-04 14:38:57
@article{95485309-8640-43aa-a81b-4b278d5efafd,
  abstract     = {{<p>We consider the Boussinesq equation on the line for a broad class of Schwartz initial data for which (i) no solitons are present, (ii) the spectral functions have generic behavior near \pm1, and (iii) the solution exists globally. In a recent work, we identified 10 main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term. In this paper, we give a proof for the formula corresponding to the sector <sup>x</sup><sub>t</sub> \in(0, \surd<sup>1</sup><sub>3</sub>).</p>}},
  author       = {{Charlier, C. and Lenells, J.}},
  issn         = {{0036-1410}},
  keywords     = {{Boussinesq equation; long-time asymptotics; Riemann-Hilbert problem}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{4104--4142}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Mathematical Analysis}},
  title        = {{BOUSSINESQ'S EQUATION FOR WATER WAVES : ASYMPTOTICS IN SECTOR V}},
  url          = {{http://dx.doi.org/10.1137/23M1587671}},
  doi          = {{10.1137/23M1587671}},
  volume       = {{56}},
  year         = {{2024}},
}