Cauchy problem for nonlinear dispersive equations and integrable systems
Project/Area Number |
26800070
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Mathematical analysis
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Research Institution | Saga University |
Principal Investigator |
Kato Takamori 佐賀大学, 工学(系)研究科(研究院), 講師 (50620639)
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | 非線形分散型 / 初期値問題 / 適切性 / 調和解析 / 可積分系 / 分散型方程式 / 非線形 / KdV方程式 / 偏微分方程式 / 非線型分散型方程式 / 漸近挙動 / 偏微分方程式論 / 非線形分散型方程式 |
Outline of Final Research Achievements |
We studied the well-poseness for the Cauchy problem of the periodic fifth order KdV equation and fifth order modified KdV equation which are completely integrable. In this study, the key idea is how to analysis the resonant parts in which the strongest nonlinear interaction concentrates. We succeeded in giving the explicit formula of the resonant pars and cancelling them by using the algebraic structure of integrable systems. Moreover, since the nonlinear terms except resonant parts were able to be regarded as the perturbation of the linearized solutions, we proved the well-posedness and unconditional uniqueness in wide function spaces.
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Report
(5 results)
Research Products
(25 results)