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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| Project Status |
Completed (Fiscal Year 2016)
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| 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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 平面孤立波 / 安定性 / 線形安定性 / レゾナンス / 安定性解析 / 平面進行波 / 長波長近似モデル / KP-II 方程式 / 平面進行波解 / line soliton / KP-II方程式 / KP-II / KdV |
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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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Report
(5 results)
Research Products
(23 results)
