Perspectives on the formation of peakons in the stochastic Camassa-Holm equation
File(s)
Accepted version
Author(s)
Bendall, Thomas M
Cotter, Colin J
Holm, Darryl D
Type
Journal Article
Abstract
A famous feature of the Camassa–Holm equation is its admission of peaked soliton solutions known as peakons. We investigate this equation under the influence of stochastic transport. Noting that peakons are weak solutions of the equation, we present a finite-element discretization for it, which we use to explore the formation of peakons. Our simulations using this discretization reveal that peakons can still form in the presence of stochastic perturbations. Peakons can emerge both through wave breaking, as the slope turns vertical, and without wave breaking as the inflection points of the velocity profile rise to reach the summit.
Date Issued
2021-06-30
Date Acceptance
2021-05-13
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2021, 477 (2250)
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
477
Issue
2250
Copyright Statement
© Crown copyright 2021.
Reproduced with the permission of the Controller of Her Majesty's Stationery Office and the Met Office.
Reproduced with the permission of the Controller of Her Majesty's Stationery Office and the Met Office.
License URL
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000661746500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
stochastic partial differential equation
nonlinear waves
finite-element discretization
GLOBAL CONSERVATIVE SOLUTIONS
DISCONTINUOUS GALERKIN METHOD
SHALLOW-WATER EQUATION
FINITE-ELEMENT METHODS
WAVE BREAKING
TRANSPORT
SCHEME
Publication Status
Published
Article Number
ARTN 20210224
Date Publish Online
2021-06-09