Journal of Nonlinear Mathematical Physics

Volume 10, Issue 4, November 2003, Pages 464 - 486

On Vortex Solutions and Links between the Weierstrass System and the Complex Sine-Gordon Equations

Authors
P. Bracken, P.P. Goldstein, A.M. Grundland
Corresponding Author
P. Bracken
Received 16 December 2002, Revised 10 February 2003, Accepted 24 February 2003, Available Online 1 November 2003.
DOI
10.2991/jnmp.2003.10.4.4How to use a DOI?
Abstract

The connection between the complex Sine and Sinh-Gordon equations associated with a Weierstrass type system and the possibility of construction of several classes of multivortex solutions is discussed in detail. We perform the Painlevé Test and analyse the possibility of deriving the Bäcklund transformation from the singularity analysis of the complex sine-Gordon equation. We make use of the analysis using the known relations for the Painlevé equations to construct explicit formulæ in terms of the Umemura polynomials which are -functions for rational solutions of the third Painlevé equation. New classes of multivortex solutions of a Weierstrass system are obtained through the use of this proposed procedure. Some physical applications are mentioned in the area of the vortex Higgs model when the complex sine-Gordon equation is reduced to coupled Riccati equations.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
10 - 4
Pages
464 - 486
Publication Date
2003/11/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2003.10.4.4How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - P. Bracken
AU  - P.P. Goldstein
AU  - A.M. Grundland
PY  - 2003
DA  - 2003/11/01
TI  - On Vortex Solutions and Links between the Weierstrass System and the Complex Sine-Gordon Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 464
EP  - 486
VL  - 10
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.4.4
DO  - 10.2991/jnmp.2003.10.4.4
ID  - Bracken2003
ER  -