Differential and Integral Equations

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

Masaya Maeda and Satoshi Masaki

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In this article, we consider the nonlinear Schrödinger equation with nonlocal nonlinearity, which is a generalized model of the Schrödinger--Poisson system (Schrödinger--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.

Article information

Differential Integral Equations, Volume 26, Number 7/8 (2013), 731-756.

First available in Project Euclid: 20 May 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]


Maeda, Masaya; Masaki, Satoshi. An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity. Differential Integral Equations 26 (2013), no. 7/8, 731--756. https://projecteuclid.org/euclid.die/1369057815

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