Global analysis of dispersion and resonance of nonlinear waves
| Project/Area Number |
21740095
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 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 |
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| Research Abstract |
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.
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Report
(5 results)
Research Products
(51 results)
