Global dynamics of nonlinear dispersive equations
| Project/Area Number |
25400159
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Osaka University (2015-2016)
Kyoto University (2013-2014) |
|---|
Principal Investigator |
|
|---|
| Research Collaborator |
Schlag Wilhelm
Krieger Joachim
Gustafson Stephen
Tsai Tai-Peng
Masmoudi Nader
Ibrahim Slim
Guo Zihua
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 非線形分散型方程式 / 解の大域挙動 / ソリトン / 基底状態 / 励起状態 / 解の爆発 / 非線形散乱理論 / 漸近安定性 / 散乱理論 / 中心安定多様体 / 臨界指数 / 国際研究者交流：フランス / 非線形波動方程式 / 大域ダイナミクス / 爆発解 / 水面波 |
|---|
| Outline of Final Research Achievements |
Concerning the global dynamics of the nonlinear Schrodinger equation, classification is given in the energy region containing two families of solitons which are very different from each other. More precisely, classification on global behavior of solutions and description of the transition are given under an energy constraint such that the ground state solitons and the first excited state solitons are contained, which are generated mainly from the interaction with the linear and the nonlinear potentials, respectively. Moreover, partial results are obtained on classification of global behavior of solutions for the generalized KdV equations, the water wave equations, the Zakharov systems and the Gross-Pitaevskii equations.
|
Report
(5 results)
Research Products
(33 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] Global dynamics of nonlinear dispersive equations2015
Author(s)
Kenji Nakanishi
Organizer
Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations
Place of Presentation
Mathematical Sciences Research Institute (アメリカ・バークレイ)
Year and Date
2015-08-27
Related Report
Int'l Joint Research / Invited
-
-
-
-
-
-
-
-
-
