AN EXAMPLE OF STABLE EXCITED STATE ON NONLINEAR SCHR?DINGER EQUATION WITH NONLOCAL NONLINEARITY

Masaya Maeda; Satoshi Masaki

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AN EXAMPLE OF STABLE EXCITED STATE ON NONLINEAR SCHR?DINGER EQUATION WITH NONLOCAL NONLINEARITY

机译：具有局部非线性的非线性Schriffinger方程的稳态激发态的一个例子

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

机译：在本文中，我们考虑具有非局部非线性的非线性Schr odinger方程，它是低维Schr？dinger-Poisson系统（Schr？dinger {Newton方程）的广义模型。我们证明了比以前的结果更广阔的空间中的全局适定性，并显示了包括激发态在内的驻波的稳定性。事实证明，具有高莫尔斯指数的稳定激发态的例子。还给出了行波型解决方案的几个示例。

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《Differential and integral equations》 |2013年第8期|共26页
作者
Masaya Maeda; Satoshi Masaki;
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原文格式 PDF
正文语种 eng
中图分类微分方程、积分方程;
关键词
NONLINEAR; SCHR?DINGER; EQUATION;

机译：非线性;Schrodinger;方程;

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1. AN EXAMPLE OF STABLE EXCITED STATE ON NONLINEAR SCHR?DINGER EQUATION WITH NONLOCAL NONLINEARITY [J] . Masaya Maeda, Satoshi Masaki Differential and integral equations . 2013,第7a8期

机译：具有局部非线性的非线性Schriffinger方程的稳态激发态的一个例子
2. Pattern formation in the nonlinear Schr?dinger equation with competing nonlocal nonlinearities [J] . F. Maucher, T. Pohl, W. Krolikowski, Optical Data Processing and Storage . 2017,第1期

机译：具有竞争非局部非线性的非线性Schr？dinger方程的模式形成。
3. Abundant excited optical breathers for a nonlinear Schr?dinger equation with variable dispersion and nonlinearity terms in inhomogenous fiber optics [J] . Yu-Lan Ma Optik: Zeitschrift fur Licht- und Elektronenoptik: = Journal for Light-and Electronoptic . 2020,第期

机译：用于非线性SCHR的丰富兴奋的光学呼吸呼吸器，具有可变分散和非线性纤维光学器件的可变分散和非线性术语
4. A survey on nonlinear Schr?dinger equation with growing nonlocal nonlinearity [C] . Masaya Maeda, Satoshi Masaki MSJ-SI International Conference "Nonlinear Dynamics in Partial Differential Equations" . 2015

机译：非线性非线性不含非线性非线性的非线性SCHR的调查
5. Studies on instability of solitary waves for nonlinear Schr?dinger equations [D] . 深谷　法良 2019

机译：非线性薛定er方程孤波不稳定性的研究
6. Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation [O] . Wei Liu, Jing Zhang, Xiliang Li 2012

机译：二维非局部非线性Schrödinger方程和非局部Klein-Gordon方程中的无赖波
7. Rogon-like solutions excited in the two-dimensional nonlocal nonlinear Schrödinger equation [O] . Yan Zhenya 2011

机译：二维非局部非线性Schrödinger方程中激发的类Rogon解

AN EXAMPLE OF STABLE EXCITED STATE ON NONLINEAR SCHR?DINGER EQUATION WITH NONLOCAL NONLINEARITY

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