Two-component higher order Camassa-Holm systems with fractional inertia operator: A geometric approach

Joachim Escher; Tony Lyons

doi:10.3934/jgm.2015.7.281

Two-component higher order Camassa-Holm systems with fractional inertia operator: A geometric approach

Joachim Escher, Tony Lyons

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensure the existence of temporally global solutions are presented. Moreover in the metric case, and for inertia operators of order higher than three, the flow is shown to be geodesically complete.

Original language	English
Pages (from-to)	281-293
Number of pages	13
Journal	Journal of Geometric Mechanics
Volume	7
Issue number	3
DOIs	https://doi.org/10.3934/jgm.2015.7.281
Publication status	Published - 01 Sep 2015
Externally published	Yes

Keywords

Diffeomorphism group
Geodesic flow
Global solutions

Access to Document

10.3934/jgm.2015.7.281

Cite this

@article{08433d7242714e7a8d0d404a1a012f96,

title = "Two-component higher order Camassa-Holm systems with fractional inertia operator: A geometric approach",

abstract = "In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensure the existence of temporally global solutions are presented. Moreover in the metric case, and for inertia operators of order higher than three, the flow is shown to be geodesically complete.",

keywords = "Diffeomorphism group, Geodesic flow, Global solutions",

author = "Joachim Escher and Tony Lyons",

note = "Publisher Copyright: {\textcopyright} American Institute of Mathematical Sciences.",

year = "2015",

month = sep,

day = "1",

doi = "10.3934/jgm.2015.7.281",

language = "English",

volume = "7",

pages = "281--293",

journal = "Journal of Geometric Mechanics",

issn = "1941-4889",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - Two-component higher order Camassa-Holm systems with fractional inertia operator

T2 - A geometric approach

AU - Escher, Joachim

AU - Lyons, Tony

N1 - Publisher Copyright: © American Institute of Mathematical Sciences.

PY - 2015/9/1

Y1 - 2015/9/1

N2 - In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensure the existence of temporally global solutions are presented. Moreover in the metric case, and for inertia operators of order higher than three, the flow is shown to be geodesically complete.

AB - In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensure the existence of temporally global solutions are presented. Moreover in the metric case, and for inertia operators of order higher than three, the flow is shown to be geodesically complete.

KW - Diffeomorphism group

KW - Geodesic flow

KW - Global solutions

UR - http://www.scopus.com/inward/record.url?scp=84938873440&partnerID=8YFLogxK

U2 - 10.3934/jgm.2015.7.281

DO - 10.3934/jgm.2015.7.281

M3 - Article

AN - SCOPUS:84938873440

VL - 7

SP - 281

EP - 293

JO - Journal of Geometric Mechanics

JF - Journal of Geometric Mechanics

SN - 1941-4889

IS - 3

ER -

Two-component higher order Camassa-Holm systems with fractional inertia operator: A geometric approach

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this