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In this article, we consider nonlinear Schr\"odinger equation with nonlocalnonlinearity which is a generalized model of the Schr\"odinger-Poisson system(Schr\"odinger-Newton equations) in low dimensions. We first prove the globalwell-posedness in wider space than in previous result and show the stability ofstanding waves including excites states. It turns out that an example of stableexcite states with high Morse index is contained. Several examples oftraveling-wave-type solutions are also given.

An example of stable excited state on nonlinear Schr\"odinger equation with nonlocal nonlinearity