Differential and Integral Equations
- Differential Integral Equations
- Volume 26, Number 7/8 (2013), 731-756.
An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity
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.
Differential Integral Equations, Volume 26, Number 7/8 (2013), 731-756.
First available in Project Euclid: 20 May 2013
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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