Studies on instability of solitary waves for nonlinear Schroedinger equations

• 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
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 非線形シュレディンガー方程式 / 孤立波 / 定在波 / 安定性 / 不安定性 / 爆発

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.

Research Products

• [Journal Article] Instability of ground states for a quasilinear Schrodinger equation (2014)
  • Author(s): Mathieu Colin, Masahito Ohta
  • Journal Title: Differential and Integral Equations Volume: 27 Pages: 613-624
  • Peer Reviewed
• [Journal Article] Instability of solitary waves for nonlinear Schrodinger equations of derivative type (2014)
  • Author(s): Masahito Ohta
  • Journal Title: SUT Journal of Mathematics Volume: 50 Pages: 399-415
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations (2012)
  • Author(s): Vladimir Georgiev, Masahito Ohta
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 64 Issue: 2 Pages: 533-548
  • DOI: 10.2969/jmsj/06420533
  • NAID: 10030740334
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed
• [Journal Article] Bifurcation from semitrivial standing waves and ground states for a system of nonlinear Schrodinger equations (2012)
  • Author(s): Mathieu Colin, Maashito Ohta
  • Journal Title: SIAM Journal on Mathematical Analysis Volume: 44 Issue: 1 Pages: 206-223
  • DOI: 10.1137/110823808
  • Peer Reviewed
• [Presentation] Stability and instability of solitary waves for nonlinear Schrodinger equations of derivative type (2014)
  • Author(s): Masahito Ohta
  • Organizer: International Conference "Asymptotic Analysis for Nonlinear Dispersive and Wave Equations" In honor of Professor Nakao Hayashi's 60th birthday
  • Place of Presentation: 大阪大学
  • Year and Date: 2014-09-10
  • Invited
• [Presentation] Strong instability of standing waves for some nonlinear Schrodinger equations (2014)
  • Author(s): Masahito Ohta
  • Organizer: RIMS研究集会「調和解析と非線形偏微分方程式」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-07-01
  • Invited
• [Presentation] Instability of solitary waves for nonlinear Schrodinger equations of derivative type (2014)
  • Author(s): Masahito Ohta
  • Organizer: Stability of Solitary Waves (Workshop)
  • Place of Presentation: Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy
  • Year and Date: 2014-05-28
  • Invited
• [Presentation] 微分型非線形シュレディンガー方程式の孤立波解の軌道不安定性
  • Author(s): 太田 雅人
  • Organizer: 非線形解析セミナー@大岡山
  • Place of Presentation: 東京工業大学
  • Invited
• [Presentation] 微分型非線形シュレディンガー方程式の孤立波解の軌道不安定性
  • Author(s): 太田 雅人
  • Organizer: 南大阪応用数学セミナー
  • Place of Presentation: 大阪市立大学
  • Invited
• [Presentation] Instability of solitary waves for nonlinear Schrodinger equations of derivative type
  • Author(s): 太田 雅人
  • Organizer: 京都大学 NLPDE セミナー
  • Place of Presentation: 京都大学理学研究科
  • Invited
• [Presentation] 非線形シュレディンガー方程式の孤立波の安定性解析
  • Author(s): 太田 雅人
  • Organizer: RIMS研究集会「非線形波動現象の数理と応用」
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] 非線形分散波動方程式の孤立波解に関する諸問題
  • Author(s): 太田雅人
  • Organizer: RIMS 共同研究「非線型現象の数理モデルに現れる近平衡解の時間的漸近挙動に関する研究」
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] Splitting methods for semilinear evolution equations with applications to nonlinear Schrodinger equations
  • Author(s): 太田雅人
  • Organizer: 第８回 非線型の諸問題
  • Place of Presentation: 宮崎県婦人会館
  • Invited
• [Presentation] Splitting methods for semilinear evolution equations with applications to nonlinear Schrodinger equations
  • Author(s): Masahito Ohta
  • Organizer: The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Orlando, Florida, USA
  • Invited
• [Remarks] Home Page of Masahito Ohta
  • URL: http://www.rs.tus.ac.jp/mohta/index.html