Conformal properties and Bäcklund transform for the associated Camassa-Holm equation

Rossen Ivanov

doi:10.1016/j.physleta.2005.07.001

Conformal properties and Bäcklund transform for the associated Camassa-Holm equation

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

Abstract

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this Letter. It is shown that the Bäcklund transform is related to the conformal properties of these equations. Some particular solutions of the associated Camassa-Holm equation are discussed also.

Original language	English
Pages (from-to)	112-118
Number of pages	7
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	345
Issue number	1-3
DOIs	https://doi.org/10.1016/j.physleta.2005.07.001
Publication status	Published - 26 Sep 2005
Externally published	Yes

Keywords

Conformal invariants
Integrable systems
Lax pair
Negatons
Positons
Schwarz derivative
Solitons

Access to Document

10.1016/j.physleta.2005.07.001

https://arrow.tudublin.ie/scschmatart/73Licence: CC BY-NC-SA

Cite this

@article{4038ab7adcb342a4a478bad472543c0e,

title = "Conformal properties and B{\"a}cklund transform for the associated Camassa-Holm equation",

abstract = "Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this Letter. It is shown that the B{\"a}cklund transform is related to the conformal properties of these equations. Some particular solutions of the associated Camassa-Holm equation are discussed also.",

keywords = "Conformal invariants, Integrable systems, Lax pair, Negatons, Positons, Schwarz derivative, Solitons",

author = "Rossen Ivanov",

year = "2005",

month = sep,

day = "26",

doi = "10.1016/j.physleta.2005.07.001",

language = "English",

volume = "345",

pages = "112--118",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

issn = "0375-9601",

publisher = "Elsevier B.V.",

number = "1-3",

}

TY - JOUR

T1 - Conformal properties and Bäcklund transform for the associated Camassa-Holm equation

AU - Ivanov, Rossen

PY - 2005/9/26

Y1 - 2005/9/26

N2 - Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this Letter. It is shown that the Bäcklund transform is related to the conformal properties of these equations. Some particular solutions of the associated Camassa-Holm equation are discussed also.

AB - Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this Letter. It is shown that the Bäcklund transform is related to the conformal properties of these equations. Some particular solutions of the associated Camassa-Holm equation are discussed also.

KW - Conformal invariants

KW - Integrable systems

KW - Lax pair

KW - Negatons

KW - Positons

KW - Schwarz derivative

KW - Solitons

UR - http://www.scopus.com/inward/record.url?scp=24644443242&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2005.07.001

DO - 10.1016/j.physleta.2005.07.001

M3 - Article

AN - SCOPUS:24644443242

SN - 0375-9601

VL - 345

SP - 112

EP - 118

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-3

ER -

Conformal properties and Bäcklund transform for the associated Camassa-Holm equation

Abstract

Keywords

Access to Document

Fingerprint

Cite this