Poisson Actions and Scattering Theory for Integrable Systems
dg-ga
2008-02-03 v1 Differential Geometry
Exactly Solvable and Integrable Systems
solv-int
Abstract
Conservation laws, heirarchies, scattering theory and B\"acklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply the theory to the ZS-AKNS nxn heirarchy (which includes the non-linear Schr\"odinger equation, modified KdV, and the n-wave equation). We also discuss a number of applications in geometry, including the sine-Gordon equation, harmonic maps, Schr\"odinger flows on Hermitian symmetric spaces, Darboux orthogonal coordinates, and isometric immerisons of one space form in another.
Cite
@article{arxiv.dg-ga/9707004,
title = {Poisson Actions and Scattering Theory for Integrable Systems},
author = {Chuu-Lian Terng and Karen Uhlenbeck},
journal= {arXiv preprint arXiv:dg-ga/9707004},
year = {2008}
}
Comments
85 pages