2016 Fiscal Year Final Research Report
Stability analysis of patterns in nonlinear dispersive equations
| Project/Area Number |
25400174
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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 | Hiroshima University (2015-2016)
Kyushu University (2013-2014) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 平面孤立波 / 安定性 / 線形安定性 / レゾナンス |
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| Outline of Final Research Achievements |
I study stability of 1-line solitons for the KP-II equation and prove their stability for polynomially decaying perturbations. This is an improvement of my former result published in 2015 which shows stability of 1-line solitons for exponentially decaying perturbations. I obtain the result by splitting a small solution of the KP-II equation from the perturbations to line solitons which ensures exponential decay of the rest of the pertrubations.
I also studied the asymptotic linear stability of planar solitary wave solutions for the Benney-Luke equation which is another 2-dimensional model of long water waves.
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| Free Research Field |
非線形偏微分方程式
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