The scattering problem for a noncommutative nonlinear Schrödinger equation

Bergfinnur Durhuus (1) , Victor Gayral (2)

1 Department of Mathematical Sciences [Copenhagen]
2 LMR - Laboratoire de Mathématiques de Reims

We investigate scattering properties of a Moyal deformed version of the nonlinear Schrödinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general initial data has a unique globally defined solution, and also has soliton solutions if the interaction potential is suitably chosen. We demonstrate how to set up a scattering framework for equations of this type, including appropriate decay estimates of the free time evolution and the construction of wave operators defined for small scattering data in the general case and for arbitrary scattering data in the rotationally symmetric case.

Mots clés: Noncommutative geometry; Scattering theory; Nonlinear Schrödinger equation

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Equations aux dérivées partielles [math.AP]

Bergfinnur Durhuus, Victor Gayral. The scattering problem for a noncommutative nonlinear Schrödinger equation. 2009. ⟨hal-00366548⟩