Action-Angle variables for the Gel'fand-Dikii flows
Analysis of PDEs
2015-06-26 v1
Abstract
Using the scattering transform for 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.
Cite
@article{arxiv.math/9712254,
title = {Action-Angle variables for the Gel'fand-Dikii flows},
author = {Richard Beals and D. H. Sattinger},
journal= {arXiv preprint arXiv:math/9712254},
year = {2015}
}