2015 Fiscal Year Final Research Report
Study of structure of solutions to Schrodinger equation from quantum-fluid point of view
Project/Area Number |
24740108
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Global analysis
|
Research Institution | Hiroshima University |
Principal Investigator |
Masaki Satoshi 広島大学, 工学(系)研究科(研究院), 准教授 (20580492)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Keywords | 非線形シュレディンガー方程式 / 分散型方程式 / KdV 方程式 / 一般化KdV方程式 / 解の長時間挙動 / 解の長時間挙動 / 最小化問題 / 最小爆発解 |
Outline of Final Research Achievements |
The first intend of the research was to focus on quantum-fluid properties of Schrodinger equations and to clarify the correspondence between blowup of solution to a nonlinear Schrodinger equation and collapse of solution of a corresponding classical fluid equation. The intended method for this analysis is a contradiction argument that construct a virtual solution from failure of a target conclusion. In this decade, there is much progress on this kind of argument. The research progresses unexpectedly and a special non-scattering solution which is minimal in a suitable sense is found for mass-subcritical equations. Behavior of the solution is completely unknown and different from any of those we knew before. I also consider generalized KdV equations and find that similar kind of threshold solution exists.
|
Free Research Field |
非線型偏微分方程式
|