Differential and Integral Equations

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

Masaya Maeda and Satoshi Masaki

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369057815

Mathematical Reviews number (MathSciNet)
MR3098985

Zentralblatt MATH identifier
1299.35284

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

Citation

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


Export citation