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Stable standing waves for Nonlinear Schr\'odinger-Poisson system with a doping profile
- Publication Year :
- 2024
-
Abstract
- This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the existence of stable standing waves by considering the associated $L^2$-minimization problem. The presence of a doping profile causes a difficulty in the proof of the strict sub-additivity. A key ingredient is to establish the strict sub-additivity by adapting a scaling and an iteration argument, which is inspired by \cite{ZZou}. When the doping profile is a characteristic function supported on a bounded smooth domain, smallness of some geometric quantity related to the domain ensures the existence of stable standing waves.
- Subjects :
- Mathematics - Analysis of PDEs
Mathematical Physics
35J20, 35B35, 35Q55
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.01842
- Document Type :
- Working Paper