Studies on instability of solitary waves for nonlinear Schroedinger equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540163
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: OHTA Masahito 東京理科大学, 理学部, 准教授 (00291394)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 非線形シュレディンガー方程式 / 孤立波 / 定在波 / 安定性

Outline of Final Research Achievements

We studied orbital instability of solitary wave solutions for a generalized nonlinear Schroedinger equation of derivative type. This equation has a two-parameter family of solitary wave solutions. We determined the borderline curve between stability and instability of solitary wave solutions in the parameter domain.
We gave a sufficient condition for strong instability of standing wave solutions for nonlinear Schroedinger equations with double power nonlinearity and for nonlinear Schroedinger equations with an attractive delta potential in one space dimension. Here, a solitary wave solution is said to be strongly unstable if there exists a solution that blows up in finite time in any small neighborhood of the solitary wave solutions.

Free Research Field

非線形偏微分方程式論