Smooth and peaked solitons of the CH equation

Darryl D. Holm; Rossen I. Ivanov

doi:10.1088/1751-8113/43/43/434003

Smooth and peaked solitons of the CH equation

Darryl D. Holm, Rossen I. Ivanov

School of Mathematics and Statistics

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

Abstract

The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann-Hilbert problem. The dispersionless limit of the CH equation and its resulting peakon solutions are examined by using an asymptotic expansion in the dispersion parameter.

Original language	English
Article number	434003
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	43
Issue number	43
DOIs	https://doi.org/10.1088/1751-8113/43/43/434003
Publication status	Published - 29 Oct 2010

Access to Document

10.1088/1751-8113/43/43/434003

Cite this

@article{3e8494a7fce44bc6a39b67564e5c462d,

title = "Smooth and peaked solitons of the CH equation",

abstract = "The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann-Hilbert problem. The dispersionless limit of the CH equation and its resulting peakon solutions are examined by using an asymptotic expansion in the dispersion parameter.",

author = "Holm, \{Darryl D.\} and Ivanov, \{Rossen I.\}",

year = "2010",

month = oct,

day = "29",

doi = "10.1088/1751-8113/43/43/434003",

language = "English",

volume = "43",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "43",

}

TY - JOUR

T1 - Smooth and peaked solitons of the CH equation

AU - Holm, Darryl D.

AU - Ivanov, Rossen I.

PY - 2010/10/29

Y1 - 2010/10/29

N2 - The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann-Hilbert problem. The dispersionless limit of the CH equation and its resulting peakon solutions are examined by using an asymptotic expansion in the dispersion parameter.

AB - The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann-Hilbert problem. The dispersionless limit of the CH equation and its resulting peakon solutions are examined by using an asymptotic expansion in the dispersion parameter.

UR - https://www.scopus.com/pages/publications/78649678927

U2 - 10.1088/1751-8113/43/43/434003

DO - 10.1088/1751-8113/43/43/434003

M3 - Article

AN - SCOPUS:78649678927

SN - 1751-8113

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 43

M1 - 434003

ER -

Smooth and peaked solitons of the CH equation

Abstract

Access to Document

Fingerprint

Cite this