On Complete Integrability of the Generalized Weierstrass System

DOI

10.2991/jnmp.2002.9.2.6How to use a DOI?

Abstract

In this paper we study certain aspects of the complete integrability of the Generlized Weierstrass system in the context of the Sinh-Gordon type equation. Using the conditional symmetry approach, we construct the Bäcklund transformation for the Generalized Weierstrass system which is determined by coupled Riccati equations. Next a linear spectral problem is found which is determined by nonsingular 2 × 2 matrices based on an sl(2, C) representation. We derive the explicit form of the Daboux transformation for the Weierstrass system. New classes of multisoliton solutions of the Generalized Weierstrass system are obtained through the use of the Bäcklund transformation and some physical applications of these results in the area of classical string theory are presented.

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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TY  - JOUR
AU  - P. Bracken
AU  - A.M. Grundland
PY  - 2002
DA  - 2002/05/01
TI  - On Complete Integrability of the Generalized Weierstrass System
JO  - Journal of Nonlinear Mathematical Physics
SP  - 229
EP  - 247
VL  - 9
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.2.6
DO  - 10.2991/jnmp.2002.9.2.6
ID  - Bracken2002
ER  -