Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2002-11-19
J. Nonlinear Math. Phys. 9, no. 2 (2002) 229-247
Nonlinear Sciences
Exactly Solvable and Integrable Systems
arxiv version is already official
Scientific paper
In this paper we study certain aspects of the complete integrability of the Generalized Weierstrass system in the context of the Sinh-Gordon type equation. Using the conditional symmetry approach, we construct the B\"{a}cklund 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 $2 \times 2$ matrices based on an $sl (2, \mathbb C)$ representation. We derive the explicit form of the Darboux transformation for the Weierstrass system. New classes of multisoliton solutions of the Generalized Weierstrass system are obtained through the use of the B\"{a}cklund transformation and some physical applications of these results in the area of classical string theory are presented.
Bracken Paul
Grundland Alfred Michel
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