Analysis of nonlinear Schroedinger equation with electromagnetic potentials

具有电磁势的非线性薛定谔方程分析

• 批准号: 22740095
• 负责人: SHIRAI Shin-ichi
• 金额: $ 0.92万
• 依托单位: Osaka Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740095/
• 关键词: 偏微分方程式; スペクトル解析; 解析学; 非線型シュレーディンガー方程式; multi-bump解の存在; 強磁場極限; 解の多重存在

The nonlinear Schroedinger equation has not only the importance as a mathematical object but the one that describes the phenomenon in physics, engineering, etc. In this research, the multiple existence of solutions and some properties of a nonlinear Schroedinger equation with magnetic field is studied mathematically. More precisely, in the case where the nonlinearity is super-linear and subcritical and the magnetic field has the bounded well, i.e., a nonempty interior of its bottom (zero set), it is shown that the equation has multiple solutions which are localized near the magnetic well and decay exponentially at spatial infinity.

非线性薛定谔方程不仅是一个重要的数学对象，而且是描述物理、工程等领域现象的方程。本文从数学上研究了一类带磁场的非线性薛定谔方程解的多重存在性及其一些性质。更确切地说，在非线性为超线性和亚临界的情况下，磁场具有有界阱，即其底部（零集）的非空内部，表明方程具有多个解，这些解在磁阱附近定域，并在空间无穷远处呈指数衰减。

项目成果

Nonlinear Schroedinger Equations with Steep Magnetic Well

陡磁阱非线性薛定谔方程

• 发表时间: 2013
• 期刊: Tokyo Journal of Mathematics
• 影响因子: 0.6
• 作者: Hsu;P.-Y. and Maekawa;Y.;Kazumasa Kuwada;H.Sunagawa;Kazuhiro Takimoto;T . Watanabe and J. Urabe;Yasunori Maekawa;Kazumasa Kuwada;砂川秀明;Takuya WATANABE and Jiichiroh URABE;Kazuhiro Takimoto;Kazumasa Kuwada;H.Sunagawa;Y. Maekawa;砂川秀明;Kazumasa Kuwada;Y. Maekawa;T . W atanabe and M.Zerzeri;Shin-ichi Shirai
• 通讯作者: Shin-ichi Shirai

Nonlinear Schrödinger Equations with Steep Magnetic Well

具有陡磁阱的非线性薛定谔方程

• DOI: 10.3836/tjm/1374497510
• 发表时间: 2013
• 作者: S. Shirai

急峻な磁場井戸をもつ非線型シュレーディンガー方程式の解の存在について

陡峭磁场井非线性薛定谔方程解的存在性

• 发表时间: 2010
• 作者: Shin-ichi;Shirai
• 通讯作者: Shirai

Multi-bump solutions to a NLS equation with steep magnetic wells

具有陡磁井的 NLS 方程的多凸点解

• 发表时间: 2011
• 作者: Shirai;Shin-ichi;Takuya WATANABE;桑田和正;前川泰則;Shin-ichi Shirai
• 通讯作者: Shin-ichi Shirai