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