1. On a nonlinear Schrödinger equation for nucleons in one space dimension
- Author
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Simona Rota Nodari, Christian Klein, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), French National Research Agency (ANR)ANR-17-CE40-0035ANR-17-CE40-0016isite BFC project NAANoDEuropean Commission778010EITAG project - FEDER de BourgogneRegion Bourgogne-Franche-ComteEUR EIPHIANR-17-EURE-0002 EIPHI, ANR-17-CE40-0035,ANuI,Approches analytiques, numériques et des systèmes intégrables pour les équations aux dérivées partielles dispersives nonlinéaires(2017), ANR-17-CE40-0016,DYRAQ,Dynamique des systèmes quantiques relativistes(2017), ANR-17-EURE-0002,EIPHI,Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité(2017), French National Research Agency (ANR)ANR-17-CE40-0035French National Research Agency (ANR)ANR-17-CE40-0016isite BFC project NAANoD European Commission778010EITAG project - FEDER de Bourgogne Region Bourgogne-Franche-Comte EUR EIPHI ANR-17-EURE-0002 EIPHI, European Project: 778010,IPaDEGAN, and Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
numerical study ,Space dimension ,Nonlinear Schrö ,010103 numerical & computational mathematics ,Nonlinear Schrödinger equations ,01 natural sciences ,Stability (probability) ,symbols.namesake ,Mathematics - Analysis of PDEs ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Mathematics - Numerical Analysis ,0101 mathematics ,[MATH]Mathematics [math] ,dinger equations ,Nonlinear Schrödinger equation ,Mathematics ,MSC 35Q55, 35C08, 65M70 ,Numerical Analysis ,Applied Mathematics ,010102 general mathematics ,Time evolution ,ground states ,Computational Mathematics ,Classical mechanics ,Modeling and Simulation ,Atomic nucleus ,symbols ,Particle ,Nucleon ,Analysis ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
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.
- Published
- 2021
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