Global dispersion of nonlinear waves

非线性波的全局色散

• 批准号: 18740072
• 负责人: NAKANISHI Kenji
• 金额: $ 2.43万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18740072/
• 关键词: 非線形波動; 分散性; 漸近解析; 散乱理論; 解の一意性; 漸近安定性; プラズマ; 超流動; 水面波; 時空大域評価; 非線形エネルギー; 双線形評価; 特異極限

様々な波動現象を普遍的に記述する非線形シュレディンガー方程式を中心に、非線形分散型方程式の解の挙動を調べた。特に、プラズマ波動の記述について高階近似モデルからの極限移行を広汎なクラスの解で示し、典型的な特解として反発性の場合に3次元平面波の漸近安定性、また球面値の場合に調和写像について漸近安定性を示した。また非線形クライン・ゴルドン方程式について散乱・爆発解の分類、非線形シュレディンガー方程式へのノルム移行、調和写像熱流における調和写像の永久振動などの結果も得た。これらの過程で、線形評価と非線形評価を相補的に組み合わせ、挙動の異なる成分間の相互作用や異なる状態への遷移を捉える手法をいくつか考案した。

There is a general record of the movement of the wave. The equation is in the center of the equation, and the equation is in the center of the equation. A description of the movement of the wave in the air, the movement of the wave is very high, the movement is limited, the solution is shown, the typical solution is closed, the 3-dimensional plane wave is close to the stability, the spherical surface is closed, and the image is written to show the near stability. The non-linear equations are classified, the non-linear equations are classified, the equations are classified, the equations are transferred, written and written, and the results of the permanent vibration test are successful. During the process, the components of the system, the components of the system, and the interaction between the components of the system, the components of the system, and the components of the system interact with each other in the process and shape of the system.

项目成果

Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions

二维和三维 Gross-Pitaevskii 方程的全局色散解

• 发表时间: 2007
• 期刊: Ann. Henri Poincare 8
• 作者: S. Gustafson;K. Nakanishi and T.-P. Tsai
• 通讯作者: K. Nakanishi and T.-P. Tsai

Asymptotic stability and pulsation of harmonic maps for the Landau-Lifshitz-Gilbert equation

Landau-Lifshitz-Gilbert 方程的谐波映射的渐近稳定性和脉动

• 发表时间: 2009
• 作者: Stephen Gustafson;Kenji Nakanishi and Tai-Peng Tsai;Kenji Nakanishi;Kenji Nakanishi
• 通讯作者: Kenji Nakanishi

Scattering for the Gross-Pitaevskii equation in three dimensions

三维 Gross-Pitaevskii 方程的散射

• 发表时间: 2008
• 作者: Stephen Gustafson;Kenji Nakanishi and Tai-Peng Tsai;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi
• 通讯作者: Kenji Nakanishi

Spectra of Linearized Operators for NLS Solitary Waves

• DOI: 10.1137/050648389
• 发表时间: 2006-11
• 期刊: SIAM J. Math. Anal.
• 作者: Shu-Ming Chang;S. Gustafson;K. Nakanishi;Tai-Peng Tsai

Scattering for the 3D Gross–Pitaevskii Equation

• DOI: 10.1007/s00220-017-3050-3
• 发表时间: 2016-11
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Zihua Guo;Z. Hani;K. Nakanishi