Radial solutions with prescribed numbers of zeros for the nonlinear Schrödinger equation with harmonic potential
Radial solutions with prescribed numbers of zeros for the nonlinear Schrödinger equation with harmonic potential
复制标题
具有谐波势的非线性薛定谔方程的具有指定零数的径向解
DOI：
10.1088/0951-7715/24/6/006
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发表时间：
2011
期刊：
影响因子：
1.7
通讯作者：
Fouad Hadj Selem
中科院分区：
文献类型：
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作者：
Fouad Hadj Selem
在本文中，我们研究了具有调和势的非线性薛定谔方程的径向对称驻波的结构，该方程在各种各样的应用中出现，并被称为Gross-Pitaevskii方程，其背景是具有抛物陷阱的玻色-爱因斯坦凝聚体。全局和局部分岔行为的确定显示存在的无限对称局域化状态。特别是，我们的理论提供了一个理论证明的存在与规定数量的零点取决于波的频率的解决方案。经过几个评论有关的临界情况下，数值计算，最后提出，以提供一个例子，已经获得的理论结果，并调查的超临界情况下，只有少数结果是已知的。
In this paper, we study the structure of radially symmetric standing waves for the nonlinear Schrödinger equation with harmonic potential, which arises in a wide variety of applications and is known as the Gross–Pitaevskii equation in the context of Bose–Einstein condensates with parabolic traps. Both global and local bifurcation behaviour are determined showing the existence of infinitely symmetric localized states. In particular, our theory provides a theoretical proof of the existence of a solution with prescribed numbers of zeros depending on the frequency of the wave. After a few remarks concerning the critical case, numerical computations are finally presented in order to provide an illustration of the theoretical results that have been obtained and also to investigate the supercritical case for which only few results are known.