Soliton Hierarchies Constructed from Involutions

Details Soliton Hierarchies Constructed from Involutions Soliton Hierarchies Constructed from Involutions

2010-10-27

arxiv.org/abs/1010.5596v1

AMS/IP Studies in Advanced Mathematics (48) 2010, pp. 367-381

Mathematics

Differential Geometry

Scientific paper

We introduce two families of soliton hierarchies: the twisted hierarchies associated to symmetric spaces. The Lax pairs of these two hierarchies are Laurent polynomials in the spectral variable. Our constructions gives a hierarchy of commuting flows for the generalized sine-Gordon equation (GSGE), which is the Gauss-Codazzi equation for n-dimensional submanifolds in Euclidean (2n-1)-space with constant sectional curvature -1. In fact, the GSGE is the first order system associated to a twisted Grassmannian system. We also study symmetries for the GSGE.

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