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

Richard Beals·D. H. Sattinger
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Abstract

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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Richard Beals, D. H. Sattinger. 1997-12-15. Action-Angle variables for the Gel'fand-Dikii flows. https://doi.org/10.1007/bf00946628

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