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Global studies on solitary waves for nonlinear dispersive equations

Research Project

Project/Area Number 18K03379
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionTokyo 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)

Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥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 / 孤立波 / 安定性 / 非線形分散型方程式
Outline of Final Research Achievements

We proved the strong instability of standing waves for a nonlinear Schroedinger eqution with an inverse power potential including the Coulomb potential in multi-dimensional space, which can be regarded as a generalization of a nonlinear Schroedinger equation with a delta-function potential in one space dimension.
Moreover, we studied the stability of solitary waves for a nonlinear Klein-Gordon equation with a delta-function potential, a generalized Boussinesq equation, a nonlinear Schroedinger equation on a star graph.

Academic Significance and Societal Importance of the Research Achievements

非線形シュレディンガー方程式や非線形クライン・ゴルドン方程式の孤立波解の安定性と不安定性を通して、非線形分散型方程式の解の大域的漸近挙動に関する新しい知見を得ることができた。
特に、さまざまなタイプの相互作用を含む非線形シュレディンガー方程式の定在波解の強い意味での不安定性を示すことにより、孤立波解の不安定性と爆発解の関係について明らかにすることができた。

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (23 results)

All 2021 2020 2019 2018 Other

All Journal Article (9 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 9 results,  Open Access: 6 results) Presentation (13 results) (of which Int'l Joint Research: 5 results,  Invited: 12 results) Remarks (1 results)

  • [Journal Article] Instability of the Solitary Waves for the Generalized Boussinesq Equations2020

    • Author(s)
      Li Bing、Ohta Masahito、Wu Yifei、Xue Jun
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 52 Issue: 4 Pages: 3192-3221

    • DOI

      10.1137/18m1199198

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Blow-up and strong instability of standing waves for the NLS-δ equation on a star graph2020

    • Author(s)
      Goloshchapova Nataliia、Ohta Masahito
    • Journal Title

      Nonlinear Analysis

      Volume: 196 Pages: 111753-111753

    • DOI

      10.1016/j.na.2020.111753

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Strong instability of standing waves for nonlinear Schrodinger equations with attractive inverse power potential2019

    • Author(s)
      Noriyoshi Fukaya, Masahito Ohta
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 56 Pages: 713-726

    • NAID

      120006768698

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Instability of standing waves for a system of nonlinear Schrodinger equations in a degenerate case2019

    • Author(s)
      Shotaro Kawahara, Masahito Ohta
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 81 Pages: 85-100

    • DOI

      10.2969/aspm/08110085

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Instability of standing waves for nonlinear Schrodinger equation with delta potential2019

    • Author(s)
      Masahito Ohta
    • Journal Title

      Sao Paulo Journal of Mathematical Sciences

      Volume: 13 Issue: 2 Pages: 465-474

    • DOI

      10.1007/s40863-019-00152-5

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stability of standing waves for a nonlinear Klein-Gordon equation with delta potentials2019

    • Author(s)
      Elek Csobo, Francois Genoud, Masahito Ohta, Julien Royer
    • Journal Title

      Journal of Differential Equations

      Volume: 268 Issue: 1 Pages: 353-388

    • DOI

      10.1016/j.jde.2019.08.015

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Strong instability of standing waves for nonlinear Schrodinger equations with a partial confinement2018

    • Author(s)
      Masahito Ohta
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 17 Issue: 4 Pages: 1671-1680

    • DOI

      10.3934/cpaa.2018080

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Strong Instability of Standing Waves for Nonlinear Schrödinger Equations with Harmonic Potential2018

    • 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
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Strong instability of standing waves with negative energy for double power nonlinear Schrodinger equations2018

    • Author(s)
      Noriyoshi Fukaya, Masahito Ohta
    • Journal Title

      SUT Journal of Mathematics

      Volume: 54 Pages: 131-143

    • NAID

      120006732564

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Stability of standing waves for cubic-quintic NLS with delta potential2021

    • Author(s)
      太田雅人
    • Organizer
      北海道大学PDEセミナー
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Strong instability of standing waves for cubic-quintic NLS with delta potential2021

    • Author(s)
      太田雅人
    • Organizer
      第38回 九州における偏微分方程式研究集会
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] 非線形シュレディンガー方程式の定在波解の不安定性と爆発解の関係2020

    • Author(s)
      太田雅人
    • Organizer
      大阪市立大学 数学研究所 談話会
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Strong instability of standing waves for cubic-quintic NLS with delta potential2020

    • Author(s)
      太田雅人
    • Organizer
      オンラインワークショップ「分散型方程式と実解析」
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] 非線形シュレディンガー方程式の定在波の不安定性2019

    • Author(s)
      太田 雅人
    • Organizer
      非線形偏微分方程式の理論と応用
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 非線形シュレディンガー方程式の基底状態の強不安定性について2019

    • Author(s)
      太田 雅人
    • Organizer
      第29回 数理物理と微分方程式
    • Related Report
      2019 Research-status Report
  • [Presentation] Instability of standing waves for nonlinear Schrodinger equations with delta potential2019

    • Author(s)
      Masahito Ohta
    • Organizer
      Workshop Recent Progress in Nonlinear Dispersive PDEs
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Instability of standing waves for nonlinear Schrodinger equations with delta potential2019

    • Author(s)
      Masahito Ohta
    • Organizer
      Workshop on PDEs in Direct and Inverse Problems 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with potential2018

    • Author(s)
      Masahito Ohta
    • Organizer
      Conference on Mathematics of Wave Phenomena, Karlsruhe Institute of Technology, Germany
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with inverse power potential2018

    • Author(s)
      Masahito Ohta
    • Organizer
      2018 Taiwan-Japan Workshop on Scattering, Dispersion, Traveling Waves, and Inverse Problems, National Cheng Kung University, Tainan, Taiwan
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Remarks on strong instability of standing waves for nonlinear Schrodinger equations2018

    • Author(s)
      Masahito Ohta
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, National Taiwan University, Taipei, Taiwan
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with Coulomb potential2018

    • Author(s)
      太田 雅人
    • Organizer
      RIMS共同研究(公開型) 保存則をもつ偏微分方程式の解の正則性,特異性および漸近挙動の研究
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Strong instability of standing waves for nonlinear Schrodinger equations with double power nonlinearity2018

    • Author(s)
      太田 雅人
    • Organizer
      第14回非線型の諸問題
    • Related Report
      2018 Research-status Report
    • Invited
  • [Remarks] Home Page of Masahito Ohta

    • URL

      https://www.rs.tus.ac.jp/mohta/

    • Related Report
      2018 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2022-01-27  

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