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Poisson Actions and Scattering Theory for Integrable Systems

Chuu-Lian Terng·Karen Uhlenbeck
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Abstract

Conservation laws, heirarchies, scattering theory and Bäcklund 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 Schrödinger equation, modified KdV, and the n-wave equation). We also discuss a number of applications in geometry, including the sine-Gordon equation, harmonic maps, Schrödinger flows on Hermitian symmetric spaces, Darboux orthogonal coordinates, and isometric immerisons of one space form in another.

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BibTeXRIS

Chuu-Lian Terng, Karen Uhlenbeck. 1997-07-07. Poisson Actions and Scattering Theory for Integrable Systems. https://arxiv.org/abs/dg-ga/9707004

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