ON A FRACTIONAL SCHRODINGER EQUATION IN THE PRESENCE OF HARMONIC POTENTIAL

被引：2

作者：

Ding, Zhiyan ^{[1
]}

Hajaiej, Hichem ^{[2
]}

机构：

[1] Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA

[2] Calif State Univ Los Angeles, Dept Math, Los Angeles, CA 90032 USA

来源：

ELECTRONIC RESEARCH ARCHIVE | 2021年 / 29卷 / 05期

关键词：

Schrodinger equation; fractional Laplacian; harmonic potential; stand-ing waves; variational methods; STANDING WAVES; VARIATIONAL APPROACH; ORBITAL STABILITY; INEQUALITIES;

D O I：

10.3934/era.2021047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish the existence of ground state solutions for a fractional Schrodinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide interesting numerical results about the dynamics and compare them with other types of Schrodinger equations [11, 18]. Our results explain the effect of each term of the Schrodinger equation: the fractional power, the power of the nonlinearity, and the harmonic potential.

引用

页码：3449 / 3469

页数：21

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