An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity

Details An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity

2011-09-13

arxiv.org/abs/1109.2653v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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

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