2011 Fiscal Year Final Research Report
Stability analysis on solitary wave solutions for systems of nonlinear wave equations
| Project/Area Number |
21540163
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Saitama University |
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Principal Investigator |
OHTA Masahito 埼玉大学, 大学院・理工学研究科, 准教授 (00291394)
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| Co-Investigator(Renkei-kenkyūsha) |
KOIKE Shigeaki 埼玉大学, 大学院・理工学研究科, 教授 (90205295)
NAGASAWA Takeyuki 埼玉大学, 大学院・理工学研究科, 教授 (70202223)
MACHIHARA Shuji 埼玉大学, 教育学部, 准教授 (20346373)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 非線形偏微分方程式 / 非線形シュレディンガー方程式 / 非線形波動方程式 / 孤立波 / 定在波 / 安定性 / 不安定性 |
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| Research Abstract |
We improved the standard theory on instability of standing wave solutions for nonlinear Schrodinger equations. In particular, we proved a new instability result for a borderline case between stability and instability. Moreover, we applied the abstract theory to a system of nonlinear Schrodinger equations related to the Raman amplification in plasma. Furthermore, under a general condition, we proved that linear instability implies nonlinear instability.
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