Global analysis of dispersion and resonance of nonlinear waves

非线性波色散和共振的全局分析

• 批准号: 21740095
• 负责人: NAKANISHI Kenji
• 金额: $ 2.75万
• 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: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740095/
• 关键词: 関数方程式; 関数解析; 実解析; 非線形波動; 波の分散性; 非線形共鳴; 解の大域挙動; 解の爆発; ソリトン; 中心安定多様体; 分散性; 漸近解析; 特異摂動; 散乱理論; 大域動力学; 散乱; 爆発; 基底状態; ワンパス定理; 初期値問題の適切性; Trudmger-Moser不等式; エネルギーの日数減衰

I constructed a theory to determine space-time behavior of general solutions for partial differential equations describing nonlinear waves, from the initial data and topological information on the solution in the phase space, and completely classified space-time dynamics up to an energy level slightly above that of the ground state. It is a mathematically rigorous description, based solely on the equation, of the mechanism of scattering, soliton and blow-up, which are typical behavior of nonlinear waves, and of transitions among them.

我构建了一个理论，根据相空间中解的初始数据和拓扑信息，确定描述非线性波的偏微分方程通解的时空行为，并将时空动力学完全分类到略高于其能量水平的基态。它是仅基于方程的数学上严格的描述，对散射、孤子和爆炸的机制（非线性波的典型行为）以及它们之间的跃迁进行了描述。

项目成果

Global dynamicsbeyond the ground energy for thefocusing nonlinear Klein-Gordonequation

聚焦非线性克莱因-戈登方程的超越地面能量的全球动力学

• 发表时间: 2011
• 作者: Stephen Gustafson;Kenji Nakanishi;Tai-Peng Tsai;奥山裕介;K. Ito;Kenji Nakanishi;奥山裕介;Kenji Nakanishi;K. Ito;Kenji Nakanishi;奥山裕介;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;Kenji Nakanishi
• 通讯作者: Kenji Nakanishi

Exponential decay for damped semilinear wave equation in the critical and the supercritical cases

临界和超临界情况下阻尼半线性波动方程的指数衰减

• 发表时间: 2009
• 作者: Stephen Gustafson;Kenji Nakanishi;Tai-Peng Tsai;奥山裕介;K. Ito;Kenji Nakanishi;奥山裕介;Kenji Nakanishi;K. Ito;Kenji Nakanishi;奥山裕介;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi
• 通讯作者: Kenji Nakanishi

Invariant Manifolds and Dispersive Hamiltonian Evolution Equations

• DOI: 10.4171/095
• 发表时间: 2011-09
• 作者: K. Nakanishi;W. Schlag

Global dynamics of the 3D Zakharov system

3D Zakharov 系统的全局动力学

• 发表时间: 2012
• 作者: Stephen Gustafson;Kenji Nakanishi;Tai-Peng Tsai;奥山裕介;K. Ito;Kenji Nakanishi;奥山裕介;Kenji Nakanishi;K. Ito;Kenji Nakanishi;奥山裕介;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi
• 通讯作者: Kenji Nakanishi

Global dynamics beyond the ground state energy for nonlinear Klein-Gordon equation

非线性 Klein-Gordon 方程的基态能量之外的全局动力学

• 发表时间: 2010
• 作者: Stephen Gustafson;Kenji Nakanishi;Tai-Peng Tsai;奥山裕介;K. Ito;Kenji Nakanishi;奥山裕介;Kenji Nakanishi;K. Ito;Kenji Nakanishi;奥山裕介;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;K. Ito;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi;Kenji Nakanishi
• 通讯作者: Kenji Nakanishi