Uniqueness and non-degeneracy for a nuclear nonlinear Schrödinger equation

Mathieu Lewin (1) , Simona Rota Nodari (2)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We prove the uniqueness and non-degeneracy of positive solutions to a cubic nonlinear Schrödinger (NLS) type equation that describes nucleons. The main difficulty stems from the fact that the mass depends on the solution itself. As an application, we construct solutions to the $\sigma$--$\omega$ model, which consists of one Dirac equation coupled to two Klein-Gordon equations (one focusing and one defocusing).

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

Mathieu Lewin, Simona Rota Nodari. Uniqueness and non-degeneracy for a nuclear nonlinear Schrödinger equation. Nonlinear Differential Equations and Applications, 2015, 22 (4), pp.673-698. ⟨hal-00987318⟩