排斥谐波势下高斯子的非唯一性和非线性不稳定性

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-07-21 DOI:10.1080/03605302.2022.2050257

R. Carles, Chunmei Su

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引用次数: 5

摘要

摘要考虑具有非色散对数非线性和排斥谐波势的Schrödinger方程。对于一个合适的系数范围，存在两个正平稳解，每一个解产生一个连续的孤立波族。这些解是高斯分布的，轨道不稳定。在这种情况下，我们还讨论了基态的概念:对于任何自然定义，基态集合都是空的。

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Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

Abstract We consider the Schrödinger equation with a nondispersive logarithmic nonlinearity and a repulsive harmonic potential. For a suitable range of the coefficients, there exist two positive stationary solutions, each one generating a continuous family of solitary waves. These solutions are Gaussian, and turn out to be orbitally unstable. We also discuss the notion of ground state in this setting: for any natural definition, the set of ground states is empty.

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.