Rotating points for the conformal NLS scattering operator

Rémi Carles (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Rémi Carles. Rotating points for the conformal NLS scattering operator. Dynamics of Partial Differential Equations, 2009, 6 (1), pp.35-51. ⟨10.4310/DPDE.2009.v6.n1.a3⟩. ⟨hal-00339952v2⟩