On a nonlinear Schrödinger equation for nucleons in one space dimension

Christian Klein (1) , Simona Rota Nodari (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We study a 1D nonlinear Schrödinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied numerically via the time evolution of perturbed ground states. In the time evolution of general localized initial data, they are shown to appear in the long time behaviour of certain cases.

Mots clés: Nonlinear Schrö; dinger equations; ground states; numerical study

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Christian Klein, Simona Rota Nodari. On a nonlinear Schrödinger equation for nucleons in one space dimension. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (2), pp.409-427. ⟨10.1051/m2an/2020086⟩. ⟨hal-02463441v2⟩