Action-Angle variables for the Gel'fand-Dikii flows

Details Action-Angle variables for the Gel'fand-Dikii flows Action-Angle variables for the Gel'fand-Dikii flows

1997-12-15

arxiv.org/abs/math/9712254v1

Zeit. Ange. Math. und Physik, vol 43, (1993), 219-242

Mathematics

Analysis of PDEs

Scientific paper

Using the scattering transform for $n^{th}$ order linear scalar operators, the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner Poisson bracket for the KdV hierarchy, is computed on the scattering side. Action-angle variables are then constructed. Using this, complete integrability is demonstrated in the strong sense. Real action-angle variables are constructed in the self-adjoint case.

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