Applications of Loop Group Factorization to Geometric Soliton Equations

Details Applications of Loop Group Factorization to Geometric Soliton Equations Applications of Loop Group Factorization to Geometric Soliton Equations

2006-11-03

arxiv.org/abs/math/0611065v1

Proceedings of the International Congress of Mathematicians, Madrid 2006, vol II, pp. 927-950

Mathematics

Differential Geometry

Scientific paper

The 1-d Schrodinger flow on 2-sphere, the Gauss-Codazzi equation for flat Lagrangian submanifolds in C^n, and the space-time monopole equation are all examples of geometric soliton equations. The linear systems with a spectral parameter (Lax pair) associated to these equations satisfy the reality condition associated to SU(n). In this article, we explain the method developed jointly with K. Uhlenbeck, that uses various loop group factorizations to construct inverse scattering transforms, Backlund transformations, and solutions to Cauchy problems for these equations.

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