Action-Angle variables for the Gel'fand-Dikii flows
Richard Beals, D. H. Sattinger
Abstract
Using the scattering transform for nth 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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