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.

我建立了一个理论来确定描述非线性波的偏微分方程的一般解的时空行为，从相空间中的解的初始数据和拓扑信息，并将时空动力学完全分类到略高于基态的能级。这是一个数学上严格的描述，完全基于方程，散射，孤子和爆破，这是典型的非线性波的行为，以及它们之间的过渡机制。

项目成果

Scattering threshold for the focusing nonlinear Klein–Gordon equation

• DOI: 10.2140/apde.2011.4.405
• 发表时间: 2010-01
• 期刊: Analysis & PDE
• 影响因子: 2.2
• 作者: S. Ibrahim;N. Masmoudi;K. Nakanishi

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