Long time behavior and singular limit for solution tononlinear dispersive equation

非线性色散方程解的长时行为和奇异极限

• 批准号: 21740122
• 负责人: SEGATA Jun-ichi
• 金额: $ 1.75万
• 依托单位: Tohoku University (2010-2012)Fukuoka University of Education (2009)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740122/
• 关键词: 非線形現象; 関数方程式論; 数理物理学; 漸近解析; 調和解析学; 流体; 漸近挙動; 調和解析; 数理理物理学

We considered the long time behavior of solutions to nonlinear dispersive partial differential equations arises in various fields of physics and engineering. Especially, we focused on solvability, scattering problem, and the stability of some special solutions called standing waves for the higher order nonlinear Schrodinger type equation arising in context of the motion of vortex filament. We also studied the semiclassical limit of Schrodinger-KdV system which describes an interaction betweenlong and short waves.

我们考虑了非线性色散偏微分方程解的长时间行为，这种现象在物理学和工程学的各个领域都有出现。特别地，我们着重讨论了涡丝运动背景下高阶非线性Schrodinger型方程的可解性、散射问题以及驻波解的稳定性.我们还研究了描述长短波相互作用的Schrodinger-KdV系统的半经典极限。