Singular Solutions of Coss-coupled EPDiff Equations: Waltzing Peakons and Compacton Pairs

Colin Cotter; Darryl Holm; Rossen Ivanov; James Percival

doi:10.21427/r7rn-r265

Singular Solutions of Coss-coupled EPDiff Equations: Waltzing Peakons and Compacton Pairs

Colin Cotter, Darryl Holm, Rossen Ivanov, James Percival

School of Mathematics and Statistics

Research output: Contribution to conference › Paper › peer-review

Abstract

We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rn). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.

Original language	English
DOIs	https://doi.org/10.21427/r7rn-r265
Publication status	Published - 2012
Event	BGSIAM'11 - Sofia, Bulgaria Duration: 1 Jan 2011 → 31 Dec 2011

Conference

Conference	BGSIAM'11
Country/Territory	Bulgaria
City	Sofia
Period	1/01/11 → 31/12/11

Keywords

EPDiff equations
Euler-Poincare equations
Lagrangian
Lie Group Diff(Rn)
cross coupled
Camassa-Holm type
peakon solutions
waltzing peakons
compacton pairs

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10.21427/r7rn-r265Licence: CC BY-NC-SA

Cite this

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title = "Singular Solutions of Coss-coupled EPDiff Equations: Waltzing Peakons and Compacton Pairs",

abstract = "We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rn). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.",

keywords = "EPDiff equations, Euler-Poincare equations, Lagrangian, Lie Group Diff(Rn), cross coupled, Camassa-Holm type, peakon solutions, waltzing peakons, compacton pairs",

author = "Colin Cotter and Darryl Holm and Rossen Ivanov and James Percival",

year = "2012",

doi = "10.21427/r7rn-r265",

language = "English",

note = "BGSIAM'11 ; Conference date: 01-01-2011 Through 31-12-2011",

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TY - CONF

T1 - Singular Solutions of Coss-coupled EPDiff Equations: Waltzing Peakons and Compacton Pairs

AU - Cotter, Colin

AU - Holm, Darryl

AU - Ivanov, Rossen

AU - Percival, James

PY - 2012

Y1 - 2012

N2 - We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rn). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.

AB - We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rn). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.

KW - EPDiff equations

KW - Euler-Poincare equations

KW - Lagrangian

KW - Lie Group Diff(Rn)

KW - cross coupled

KW - Camassa-Holm type

KW - peakon solutions

KW - waltzing peakons

KW - compacton pairs

U2 - 10.21427/r7rn-r265

DO - 10.21427/r7rn-r265

M3 - Paper

T2 - BGSIAM'11

Y2 - 1 January 2011 through 31 December 2011

ER -

Singular Solutions of Coss-coupled EPDiff Equations: Waltzing Peakons and Compacton Pairs

Abstract

Conference

Keywords

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Cite this