Study on solitary wave solutions for nonlinear dispersive wave equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04968
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: Ohta Masahito 東京理科大学, 理学部第一部数学科, 教授 (00291394)
• Co-Investigator(Renkei-kenkyūsha): KATO Keiichi 東京理科大学, 理学部, 教授 (50224499)
• Research Collaborator: FUKAYA Noriyoshi ; KAWAHARA Shotaro
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 非線形シュレディンガー方程式 / 調和ポテンシャル / 定在波 / 孤立波 / 安定性

Outline of Final Research Achievements

We studied a system of nonlinear Schroedinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions were studied for both non-degenerate and degenerate cases. We also studied the instability of solitary wave solutions in endpoint case. Moreover, we proved the strong instability of standing wave solutions for nonlinear Schroedinger equations with a harmonic potential and with a partial confinement.

Free Research Field

非線形偏微分方程式論