Dynamics of solutions for nonlinear dispersive equation
| Project/Area Number |
21540220
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Kyushu University |
|---|
Principal Investigator |
MIZUMACHI Tetsu 九州大学, 大学院・数理学研究院, 准教授 (60315827)
|
|---|
| Project Period (FY) |
2009 – 2012
|
| Project Status |
Completed (Fiscal Year 2012)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 孤立波 / 安定性 / 非線形分散型方程式 / 平面進行波 / KP方程式 / KP-II方程式 / line-soliton / 1次元Benney-Luke / ソリトンの安定性 / KP-II / L^2安定性 / 一次元非線形シュレディンガー方程式 / Fermi-Pasta-Ulamの格子模型 / 多ソリトン |
|---|
| 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.
|
Report
(5 results)
Research Products
(21 results)
