Rotating points for the conformal NLS scattering operator
Analysis of PDEs
2009-02-12 v2 Mathematical Physics
math.MP
Abstract
We consider the nonlinear Schrodinger equation, with mass-critical nonlinearity, focusing or defocusing. For any given angle, we establish the existence of infinitely many functions on which the scattering operator acts as a rotation of this angle. Using a lens transform, we reduce the problem to the existence of a solution to a nonlinear Schrodinger equation with harmonic potential, satisfying suitable periodicity properties. The existence of infinitely many such solutions is proved thanks to a constrained minimization problem.
Cite
@article{arxiv.0811.3121,
title = {Rotating points for the conformal NLS scattering operator},
author = {Rémi Carles},
journal= {arXiv preprint arXiv:0811.3121},
year = {2009}
}
Comments
Some typos fixed, references added