Volume 55, Number 2, March-April 2021
|Page(s)||409 - 427|
|Published online||15 March 2021|
On a nonlinear Schrödinger equation for nucleons in one space dimension
Institut de Mathématiques de Bourgogne, UMR 5584 Université de Bourgogne-Franche-Comté, 9 Avenue Alain Savary, 21078 Dijon Cedex, France
* Corresponding author: Christian.Klein@u-bourgogne.fr
Accepted: 13 December 2020
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.
Mathematics Subject Classification: 35Q55 / 35C08 / 65M70
Key words: Nonlinear Schrödinger equations / ground states / numerical study
© The authors. Published by EDP Sciences, SMAI 2021
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