Dynamics of Partial Differential Equations

Volume 6 (2009)

Number 1

Rotating points for the conformal NLS scattering operator

Pages: 35 – 51

DOI: https://dx.doi.org/10.4310/DPDE.2009.v6.n1.a3

Author

Rémi Carles (Département de mathématiques Université Montpellier 2, Montpellier, France)

Abstract

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.

Keywords

rotating points, nonlinear Schrödinger equation, scattering operator, harmonic potential

2010 Mathematics Subject Classification

35-xx

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Published 1 January 2009