Dynamics of Partial Differential Equations
Volume 6 (2009)
Rotating points for the conformal NLS scattering operator
Pages: 35 – 51
We consider the nonlinear Schrödinger 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 Schrödinger equation with harmonic potential, satisfying suitable periodicity properties. The existence of infinitely many such solutions is proved thanks to a constrained minimization problem.
rotating points, nonlinear Schrödinger equation, scattering operator, harmonic potential
2010 Mathematics Subject Classification