Perspectives on the formation of peakons in the stochastic Camassa-Holm equation

被引：7

作者：

Bendall, Thomas M. ^{[1
,2
]}

Cotter, Colin J. ^{[2
]}

Holm, Darryl D. ^{[2
]}

机构：

[1] Dynam Res, Met Off, Exeter, Devon, England

[2] Imperial Coll, Math Dept, London, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2021年 / 477卷 / 2250期

基金：

英国工程与自然科学研究理事会;

关键词：

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;

D O I：

10.1098/rspa.2021.0224

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：18

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