Symmetries of KdV and Loop Groups

Details Symmetries of KdV and Loop Groups Symmetries of KdV and Loop Groups

1996-06-13

arxiv.org/abs/solv-int/9606004v1

Physics

High Energy Physics

High Energy Physics - Theory

36 pages (sorry), LaTeX using a4 documentstyle

Scientific paper

A simple version of the Segal-Wilson map from the SL(2,C) loop group to a class of solutions of the KdV hierarchy is given, clarifying certain aspects of this map. It is explained how the known symmetries, including Backlund transformations, of KdV arise from simple, field independent, actions on the loop group. A variety of issues in understanding the algebraic structure of Backlund transformations are thus resolved.

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