Abstract
In this article, we consider the nonlinear Schrödinger equation with nonlocal nonlinearity, which is a generalized model of the Schrö dinger{Poisson system (Schrodinger{Newton equations) in low dimensions. We prove global well-posedness in a wider space than in previous results and show the stability of standing waves including excited states. It turns out that an example of stable excited states with high Morse index is contained. Several examples of traveling-wave-type solutions are also given.
| Original language | English |
|---|---|
| Pages (from-to) | 731-756 |
| Number of pages | 26 |
| Journal | Differential and Integral Equations |
| Volume | 26 |
| Issue number | 7-8 |
| Publication status | Published - 2013 Jul 1 |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics