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Acta Applicandae Mathematica

, Volume 92, Issue 1, pp 63–76 | Cite as

The Generalized Weierstrass System for Nonconstant Mean Curvature Surfaces and the Nonlinear Sigma Model

  • Paul BrackenEmail author
Article

Abstract

A study of the generalized Weierstrass system which can be used to induce mean curvature surfaces in three-dimensional Euclidean space is presented. A specific transformation is obtained which reduces the initial system to a two-dimensional Euclidean nonlinear sigma model. Some aspects of integrability are discussed, in particular, a connection with a version of the sinh-Gordon equation is established. Finally, some specific solutions are given and a systematic way of calculating multisoliton solutions is presented.

Key words

Weirstrass system sinh-Gordon equation Euclidean space mean curvature 

Mathematics Subject Classifications (2000)

35Q51 53A10 

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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TexasEdinburgUSA

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