Volume 11, Issue 2, May 2004, Pages 164 - 179
A Generalization of the Sine-Gordon Equation to 2 + 1 Dimensions
Authors
P.G. Estévez, J. Prada
Corresponding Author
P.G. Estévez
Received 8 July 2003, Accepted 9 October 2003, Available Online 1 May 2004.
- DOI
- 10.2991/jnmp.2004.11.2.3How to use a DOI?
- Abstract
The Singular Manifold Method (SMM) is applied to an equation in 2 + 1 dimensions [13] that can be considered as a generalization of the sine-Gordon equation. SMM is useful to prove that the equation has two Painlevé branches and, therefore, it can be considered as the modified version of an equation with just one branch, that is the AKNS equation in 2 + 1 dimensions. The solutions of the former split as linear superposition of two solutions of the second, related by a Bäcklund-gauge transformtion. Solutions of both equations are obtained by means of an algorithmic procedure derived from these transformations.
- 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.G. Estévez AU - J. Prada PY - 2004 DA - 2004/05/01 TI - A Generalization of the Sine-Gordon Equation to 2 + 1 Dimensions JO - Journal of Nonlinear Mathematical Physics SP - 164 EP - 179 VL - 11 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2004.11.2.3 DO - 10.2991/jnmp.2004.11.2.3 ID - Estévez2004 ER -