Abstract
The Dirac operator enters into zero curvature representation for the cubic nonlinear Schrodinger equation. We introduce and study a conformal map from the upper half-plane of the spectral parameter of the Dirac operator into itself. The action variables turn out to be limiting boundary values of the imagi- nary part of this map. We describe the image of the momentum map (convexity theorem) in the simplest case of a potential from the Schwartz class. We apply this description to the invariant manifolds for the nonlinear Schrodinger equation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.