多维三次五次薛定谔方程的基态稳定性

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-10-06 DOI:10.1051/m2an/2022085

R. Carles, C. Klein, Christof Sparber

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引用次数: 3

摘要

摘要我们考虑了二维和三维中具有聚焦三次项和散焦五次非线性的非线性Schr¨odinger方程。本文主要研究的是基态孤立波的轨道稳定性问题。我们回顾能量最小化和作用最小化基态的概念，并证明，一般来说，两者必须被认为是不等价的。我们用数值方法研究了径向对称情况下最小作用基态的轨道稳定性，从而证实了已有的猜想或引出了新的猜想。

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On ground state (in-)stability in multi-dimensional cubic-quintic Schrodinger equations

Abstract. We consider the nonlinear Schr¨odinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The main interest of this article is the problem of orbital (in-)stability of ground state solitary waves. We recall the notions of energy minimizing versus action minimizing ground states and prove that, in general, the two must be considered as nonequivalent. We numerically investigate the orbital stability of least action ground states in the radially symmetric case, confirming existing conjectures or leading to new ones.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.