2020/10/02 by Riccardo Adami, Adami, Riccardo, Takaaki Nakamura +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum Chromodynamics and Particle Interactions #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2010.00895
openalex publication_date 2020/10/02 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We analyse the existence and the stability of the ground states of the one-dimensional nonlinear Schrödinger equation with a focusing power nonlinearity and a defect located at the origin. In this paper a ground state is defined as a global minimizer of the action functional on the Nehari manifold and the defect considered is a Fülöp-Tsutsui δ type, namely a δ condition that allows discontinuities. The existence of ground states is proved by variational techniques, while the stability results from the Grillakis-Shatah-Strauss theory.