2012 Fiscal Year Final Research Report
Dynamics of solutions for nonlinear dispersive equation
| Project/Area Number |
21540220
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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 |
Global analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
MIZUMACHI Tetsu 九州大学, 大学院・数理学研究院, 准教授 (60315827)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 孤立波 / 安定性 / 非線形分散型方程式 |
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| Research Abstract |
I study stability of solitary waves for long wave models using their monotonicity preoperty. I show that modulations of the line soliton for the KP-II equation can be described a system of the Burgers equation and prove the stability of line soliton solution. I also prove stability of multi solitary waves of the Fermi-Pasta-Ulam lattices in the KdV limit and solitary wave solutions of the Benney-Luke equation which is a kind of bidirectional models akin to the Boussinesq systems. In a joint work with Tzvetkov, we show that stability of line soliton solutions for the KP-II equation in L^2(R_x×T_y) is equivalent to the stability of the null solution by using the Miura transformation and obtain L^2(R_x×T_y) stability of line solitons. The idea was tranfered to 1D cubic NLS in a joint work with Pelinovsky.
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Research Products
(9 results)
