Study on solitary wave solutions for nonlinear dispersive wave equations

• 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
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2016: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• 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 / 不安定性

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.

Research Products

• [Int'l Joint Research] 天津大学(中国)
• [Int'l Joint Research] ポール・サバティエ大学(フランス)
• [Int'l Joint Research] サンパウロ大学(ブラジル)
• [Journal Article] Strong Instability of Standing Waves for Nonlinear Schrödinger Equations with Harmonic Potential (2018)
  • Author(s): Masahito Ohta
  • Journal Title: Funkcialaj Ekvacioj Volume: 61 Issue: 1 Pages: 135-143
  • DOI: 10.1619/fesi.61.135
  • NAID: 130006726035
  • ISSN: 0532-8721
  • Peer Reviewed / Open Access
• [Journal Article] Strong instability of standing waves for nonlinear Schrodinger equations with a partial confinement (2018)
  • Author(s): Masahito Ohta
  • Journal Title: Communications on Pure and Applied Analysis Volume: 17 Issue: 4 Pages: 1671-1680
  • DOI: 10.3934/cpaa.2018080
  • Peer Reviewed / Open Access
• [Journal Article] Instability of solitary wave solutions for derivative nonlinear Schrodinger equation in endpoint case (2017)
  • Author(s): Cui Ning, Masahito Ohta, Yifei Wu
  • Journal Title: JOURNAL OF DIFFERENTIAL EQUATIONS Volume: 262 Issue: 3 Pages: 1671-1689
  • DOI: 10.1016/j.jde.2016.10.020
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Strong instability of standing waves for nonlinear Schrodinger equations with a delta potential (2016)
  • Author(s): Masahito Ohta, Takahiro Yamaguchi
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B56 Pages: 79-92
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Strong instability of standing waves for nonlinear Schrodinger equations with double power nonlinearity (2015)
  • Author(s): Masahito Ohta, Takahiro Yamaguchi
  • Journal Title: SUT Journal of Mathematics Volume: 51 Pages: 49-58
  • NAID: 120006397882
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with a partial confinement (2018)
  • Author(s): Masahito Ohta
  • Organizer: Workshop Critical exponent and nonlinear evolution equations 2018
  • Int'l Joint Research / Invited
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with harmonic potential (2017)
  • Author(s): Masahito Ohta
  • Organizer: 第6回「ハミルトン系とその周辺」研究集会
  • Place of Presentation: 京都大学 吉田キャンパス
  • Year and Date: 2017-03-09
  • Int'l Joint Research / Invited
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with a partial confinement (2017)
  • Author(s): Masahito Ohta
  • Organizer: RIMS Workshop Nonlinear Wave and Dispersive Equations
  • Int'l Joint Research / Invited
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with a partial confinement (2017)
  • Author(s): 太田 雅人
  • Organizer: 日本数学会・2017年度 秋季総合分科会 函数方程式論分科会
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with a partial confinement (2017)
  • Author(s): Masahito Ohta
  • Organizer: Third Workshop on Nonlinear Dispersive Equations
  • Int'l Joint Research / Invited
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with harmonic potential (2016)
  • Author(s): 太田 雅人
  • Organizer: 広島数理解析セミナー
  • Place of Presentation: 広島大学 理学部
  • Year and Date: 2016-10-28
  • Invited
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with harmonic potential (2016)
  • Author(s): 太田 雅人
  • Organizer: 日本数学会 2016年度 秋季総合分科会 函数方程式論分科会
  • Place of Presentation: 関西大学 千里山キャンパス
  • Year and Date: 2016-09-18
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with a harmonic potential (2016)
  • Author(s): Masahito Ohta
  • Organizer: Mathematical Analysis for Stability in Nonlinear Dynamics‐in honor of Professor Vladimir Georgiev on his 60th birthday‐
  • Place of Presentation: 北海道大学
  • Year and Date: 2016-08-26
  • Int'l Joint Research / Invited
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with harmonic potential (2016)
  • 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 数学教室
  • Year and Date: 2016-07-01
  • Invited
• [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with harmonic potential (2016)
  • Author(s): 太田 雅人
  • Organizer: 大阪大学 微分方程式セミナー
  • Place of Presentation: 大阪大学 理学研究科 数学教室
  • Year and Date: 2016-06-03
  • Invited
• [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations with cubic nonlinearity (2015)
  • Author(s): Masahito Ohta
  • Organizer: Workshop on "Quasilinear and nonlocal nonlinear Schrodinger equations"
  • Place of Presentation: Wolfgang Pauli Institute Vienna, Austria
  • Year and Date: 2015-10-01
  • Int'l Joint Research / Invited
• [Presentation] Instability of standing waves for a system of nonlinear Schrodinger equations in a degenerate case (2015)
  • Author(s): 太田 雅人
  • Organizer: 金沢解析研究会 2015
  • Place of Presentation: 金沢大学サテライト・プラザ
  • Year and Date: 2015-08-27
  • Invited
• [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations with cubic nonlinearity (2015)
  • Author(s): Masahito Ohta
  • Organizer: The 10th International ISAAC Congress
  • Place of Presentation: University of Macau, China
  • Year and Date: 2015-08-04
  • Int'l Joint Research / Invited
• [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations in a degenerate case (2015)
  • Author(s): 太田 雅人
  • Organizer: RIMS 共同研究「非線型現象のモデルに潜む未踏査数理構造の探究-基礎数理と応用 の協働-」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-07-28
  • Invited
• [Remarks] Home Page of Masahito Ohta
  • URL: http://www.rs.tus.ac.jp/mohta/index.html
• [Remarks] 東京理科大学 理学部第一部数学科 太田研究室ホームページ
  • URL: http://www.tus.ac.jp/fac_grad/p/index.php?6652
• [Funded Workshop] Nonlinear Wave and Dispersive Equations, Kyoto 2016 (2016)
  • Place of Presentation: 京都大学 理学研究科
  • Year and Date: 2016-09-06