Applications of loop group factorization to geometric soliton equations

• Autores: Chuu-Lian Terng
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé, Javier Soria de Diego, Juan Luis Varona Malumbres, Joan Verdera, Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 927-950
• Idioma: inglés
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• Resumen

  • The 1-d Schrödinger flow on S2, the Gauss�Codazzi equation for flat Lagrangian submanifolds in R2n, 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, Bäcklund transformations, and solutions to Cauchy problems for these equations.