2016 Fiscal Year Final Research Report
Global dynamics of nonlinear dispersive equations
| Project/Area Number |
25400159
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Osaka University (2015-2016)
Kyoto University (2013-2014) |
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Principal Investigator |
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| Research Collaborator |
Schlag Wilhelm
Krieger Joachim
Gustafson Stephen
Tsai Tai-Peng
Masmoudi Nader
Ibrahim Slim
Guo Zihua
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| 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 |
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| 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.
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| Free Research Field |
偏微分方程式論
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