Poisson Actions and Scattering Theory for Integrable Systems

  title={Poisson Actions and Scattering Theory for Integrable Systems},
  author={C. L. Terng and Karen Uhlenbeck},
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 first find a simple model Poisson group action that contains flows for systems with a Lax pair whose terms all decay on R. B… CONTINUE READING
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