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

Masaya Maeda; Satoshi Masaki

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

Masaya Maeda, Satoshi Masaki

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	731-756
Number of pages	26
Journal	Differential and Integral Equations
Volume	26
Issue number	7-8
Publication status	Published - 2013 Jul 1

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "In this article, we consider the nonlinear Schr{\"o}dinger equation with nonlocal nonlinearity, which is a generalized model of the Schr{\"o} dinger{Poisson system (Schrodinger{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.",

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AU - Masaki, Satoshi

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N2 - In this article, we consider the nonlinear Schrödinger equation with nonlocal nonlinearity, which is a generalized model of the Schrö dinger{Poisson system (Schrodinger{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.

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

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