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@article{Bendall:2021:10.1098/rspa.2021.0224,
author = {Bendall, TM and Cotter, CJ and Holm, DD},
doi = {10.1098/rspa.2021.0224},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
title = {Perspectives on the formation of peakons in the stochastic Camassa-Holm equation},
url = {http://dx.doi.org/10.1098/rspa.2021.0224},
volume = {477},
year = {2021}
}

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TY  - JOUR
AB  - 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.
AU  - Bendall,TM
AU  - Cotter,CJ
AU  - Holm,DD
DO  - 10.1098/rspa.2021.0224
PY  - 2021///
SN  - 1364-5021
TI  - Perspectives on the formation of peakons in the stochastic Camassa-Holm equation
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2021.0224
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000661746500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://royalsocietypublishing.org/doi/full/10.1098/rspa.2021.0224
UR  - http://hdl.handle.net/10044/1/92498
VL  - 477
ER  -

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