Soliton Hierarchies Constructed from Involutions
Differential Geometry
2010-10-28 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1010.5596,
title = {Soliton Hierarchies Constructed from Involutions},
author = {Chuu-Lian Terng},
journal= {arXiv preprint arXiv:1010.5596},
year = {2010}
}