Relations between properties of solutions and geometric symmetry of solutions for nonlinear wave and dispersive equations

非线性波和色散方程解的性质与解的几何对称性之间的关系

• 批准号: 19204012
• 负责人: TSUTSUMI Yoshio
• 金额: $ 26.79万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-19204012/
• 关键词: 非線形波動・分散型方程式; 初期値問題の適切性・不適切性; 無条件一意性; 解の漸近挙動; フーリエ制限法; シュレディンガー写像方程式; 調和写像の熱流; 調和写像の安定性; 解の無限振動; Lugiato-Lefever方程式; 解の分岐; 安定定常解; 中心多様体縮約; 函数方程式論; 函数解析学; 実関数論; 数理物理学; 非線形分散型方程式; 初期値問題の適切性; 非線形相互作用の構造; 定常解の分岐; 空洞ソリトン; 安定性・不安定性; 修正KdV

The research results are as follows.(1) We proved the stability and instability of vortices for the harmonic map heat-flows, the Landau-Lifshitz equations and the Schrodinger maps.(2) We proved the unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schrodinger with powernonlinearity.(3) We obtained the results about the linear stability and the linear instability of stationary solution bifurcating from the constant stationary solution for the Lugiato-Lefever equation, which is the nonlinear Schrodinger equation with damping and forcing.

研究结果如下。（1）我们证明了谐波热量热量，Landau-Lifshitz方程和Schrodinger地图的涡旋的稳定性和不稳定。（2）我们证明了解决方案的cauchy Schrodinger稳定性的无条件解决方案解决方案的无条件唯一性。从lugiato-lefever方程的恒定固定溶液分叉，这是具有阻尼和强迫的非线性schrodinger方程。

项目成果

LOCAL WELL-POSEDNESS IN LOW REGULARITY OF THE MKDV EQUATION WITH PERIODIC BOUNDARY CONDITION

• DOI: 10.3934/dcds.2010.28.1635
• 发表时间: 2010-12-01
• 期刊: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
• 影响因子: 1.1
• 作者: Nakanishi, Kenji;Takaoka, Hideo;Tsutsumi, Yoshio
• 通讯作者: Tsutsumi, Yoshio

A database schema for the analysis of global dynamics of multiparameter systems, SIAM

用于分析多参数系统全局动态的数据库模式，SIAM

• 发表时间: 2009
• 期刊: J. Appl. Dyn. Syst. 8
• 作者: Z. Arai;W. Kalies;H. Kokubu;K. Mischaikow;H. Oka;P. Pilarczyk
• 通讯作者: P. Pilarczyk

Scattering for the two-dimensional energy-critical wave equation

• DOI: 10.1215/00127094-2009-053
• 发表时间: 2009-11
• 期刊: Duke Mathematical Journal
• 影响因子: 2.5
• 作者: S. Ibrahim;M. Majdoub;N. Masmoudi;K. Nakanishi

Global dispersive solutions of 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
• 作者: S. Gustafson;K. Nakanishi and T.-P. Tsai
• 通讯作者: K. Nakanishi and T.-P. Tsai

Time decay of solution for the KdV equation with multiplicative space-time noise

具有乘性时空噪声的 KdV 方程解的时间衰减

• 发表时间: 2008
• 期刊: Differential and Integral Equations 21
• 作者: Y.Nagahata;N.Yoshida;T.Sugawa;Y. Tsutsumi
• 通讯作者: Y. Tsutsumi