Analysis of dispersive wave, solitary wave and their interactions for nonlinear dispersive equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 25707004
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Partial Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Tohoku University
• Principal Investigator: Segata Jun-ichi 東北大学, 理学研究科, 准教授 (90432822)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 関数方程式論 / 数理物理学 / 漸近解析 / 調和解析学 / 流体

Outline of Final Research Achievements

In this research, we study the long time behavior of solutions to the nonlinear dispersive equations such as the generalized KdV equation and the vortex filament equation from the point of view of how dispersive wave and solitary wave would affect the long time behavior of solution. We construct a minimal non-scattering solution, which plays an important role in the classification of solutions for the mass sub-critical KdV equation. We also prove the stability of soliton for the vortex filament equation, and the long range scattering for the nonlinear Schrodinger equation with delta potential and the nonlinear Klein-Gordon equation.

Free Research Field

非線形分散型方程式