• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

STUDIES ON STABILITY OF SOLITARY WAVES AND BLOWUP OF SOLUTIONS FORNONLINEAR WAVE EQUATIONS

Research Project

Project/Area Number 18540161
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSaitama University

Principal Investigator

OHTA Masahito  Saitama University, 大学院・理工学研究科, 准教授 (00291394)

Co-Investigator(Kenkyū-buntansha) 小池 茂昭  埼玉大学, 理工学研究科, 教授 (90205295)
長澤 壯之  埼玉大学, 理工学研究科, 教授 (70202223)
町原 秀二  埼玉大学, 教育学部, 准教授 (20346373)
Co-Investigator(Renkei-kenkyūsha) KOIKE Shigeaki  埼玉大学, 大学院・理工学研究科, 教授 (90205295)
NAGASAWA Takeyuki  埼玉大学, 大学院・理工学研究科, 教授 (70202223)
MACHIHARA Shuji  埼玉大学, 教育学部, 准教授 (20346373)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥600,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywords非線形シュレディンガー方程式 / 非線形クライン・ゴルドン方程式 / 定在波解 / 非線形波動 / 安定性解析 / 爆発問題 / 非線形偏微分方程式 / 孤立波 / 変分法 / Ostrovsky方程式 / 安定性 / 非線形波動方程式 / 爆発 / 定在波
Research Abstract

消散項をもつ非線形シュレディンガー方程式の爆発問題に関して、テネシー大学のGrozdena Todorova 氏と共同研究を行った。また、湯川型相互作用をもつ空間3次元のクライン・ゴルドン・シュレディンガー方程式系の定在波解の安定性について、菊池弘明氏と共同研究を行った。さらに、3波相互作用をもつ非線形シュレディンガー方程式系の孤立波解の安定性に関して、ボルドー大学の Mathieu Colin 氏、Thierry Colin氏と共同研究を行った

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (31 results)

All 2009 2008 2007 2006 Other

All Journal Article (18 results) (of which Peer Reviewed: 14 results) Presentation (10 results) Remarks (3 results)

  • [Journal Article] Instability of standing waves for the Klein-Gordon-Schrodinger system2008

    • Author(s)
      Hiroaki Kikuchi and Masahito Ohta
    • Journal Title

      Hokkaido Mathematical Journal 37

      Pages: 735-748

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear Schrodingerequation with a point defect, Annales del'Institut Henri Poincare2008

    • Author(s)
      Reika Fukuizumi, Masahito Ohta and Tohru Ozawa
    • Journal Title

      Analyse NonLineaire 25

      Pages: 837-845

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability ofsolitary waves for the Ostrovsky equation2008

    • Author(s)
      Yue Liu, Masahito Ohta
    • Journal Title

      Proceedings of the AmericanMathematical Society 136

      Pages: 511-517

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability of solitary waves for the Ostrovsky equation2008

    • Author(s)
      Yue Liu, Masahito Ohta
    • Journal Title

      Proceedings of the American Mathematical Society 136

      Pages: 511-517

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear Schrodinger equation with.a point defect2008

    • Author(s)
      Reika Fukuizumi, Masahito Ohta, Tohru Ozawa
    • Journal Title

      Annales de 1'Institut Henri Poincar, Analyse Non Lineaire 25

      Pages: 837-845

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Instability of standing ,waves for the Klein-Gordon-Schrodinger system2008

    • Author(s)
      Hiroaki Kikuchi, Masahito Ohta
    • Journal Title

      Hokkaido Mathematical Journal 37

      Pages: 735-748

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong instability of standingwaves for nonlinear Klein-Gordonequations and solitary waves forgeneralized Boussinesq equations2007

    • Author(s)
      Yue Liu, Masahito Ohta and GrozdenaTodorova
    • Journal Title

      Annales de l'Institut Henri Poincare, Analyse Non Lineaire 24

      Pages: 539-548

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness of positive solutions to scalarfield equations with harmonic potential2007

    • Author(s)
      Munemitsu Hirose and Masahito Ohta
    • Journal Title

      Funkcialaj Ekvacioj 50

      Pages: 67-100

    • NAID

      130000140681

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Strong instability of standing waves forthe nonlinear Klein-Gordon equation andthe Klein-Gordon-Zakharov system2007

    • Author(s)
      Masahito Ohta and Grozdena Todorova
    • Journal Title

      SIAM Journal on Mathematical Analysis 38

      Pages: 1912-1931

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Strong instability of standing waves for nonlinear Klein-Gordon equations and solitary waves for generalized Boussinesq equations2007

    • Author(s)
      Yue Liu, Masahito Ohta, GTozdena Todorova
    • Journal Title

      Annales de lInstitut Henri Pgincare, Analyse Non Lineaire 24

      Pages: 539-548

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness of positive solutions to scalar field equations with harmonic potential2007

    • Author(s)
      Munemitsu Hirose, Masahito Ohta
    • Journal Title

      Funkcialaj Ekvacioj 50

      Pages: 67-100

    • NAID

      130000140681

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong in stability of standing waves for the nonlineqr Klein-Gordon equation and the Klein-Gordon-Zakharov system2007

    • Author(s)
      Masahito Ohta, Grozdena Todorova
    • Journal Title

      SIAM Joumal on Mathematical Analysis 38

      Pages: 1912-1931

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blowup for systems of semilinear waveequations in two space dimensions2006

    • Author(s)
      Mathieu Colin and Masahito Ohta
    • Journal Title

      Hokkaido Mathematical Journal 35

      Pages: 697-717

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability of solitary waves for derivativenonlinear Schrodinger equation2006

    • Author(s)
      Mathieu Colin and Masahito Ohta
    • Journal Title

      Annalesde l'Institut Henri Poincare, Analyse NonLineaire 23

      Pages: 753-764

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blowup for systems of semilinear wave equations in two space dimensions2006

    • Author(s)
      Hideo Kubo, Masahito Ohta
    • Journal Title

      Hokkaido Mathematical Jouranl 35.3

      Pages: 697-717

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability of solitary waves for derivative nonlinear Schrodiner equation2006

    • Author(s)
      Mathieu Colin, Masahito Ohta
    • Journal Title

      Annales de l'Institut Henri Poincare, Analyse Non Lineaire 23.5

      Pages: 753-764

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the existence of solutions of the Helfrich flow and its center manifold near spheres2006

    • Author(s)
      Yoshihiko Kosaka, Takeyuki Nagasawa
    • Journal Title

      Differential and Integral Equations 19.2

      Pages: 121-142

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Instability of standing waves for nonlinear Klein-Gordon equation and related system2006

    • Author(s)
      Masahito Ohta, Grozdena Todorova
    • Journal Title

      GAKUTO International Series, Mathematical Sciences and Applications 26

      Pages: 189-200

    • Related Report
      2006 Annual Research Report
  • [Presentation] 3 波相互作用をもつ非線形シュレディンガー方程式系の定在波解の不安定性2009

    • Author(s)
      太田 雅人
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
    • Related Report
      2008 Final Research Report
  • [Presentation] 3波相互作用をもつ非線形シュレディンガー方程式系の定在波解の不安定性2009

    • Author(s)
      太田雅人
    • Organizer
      日本数学会2009年度年会函数方程式論分科会
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2009-03-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] Instability of standingwaves for a system of nonlinearSchrodinger equations with three-waveinteraction2009

    • Author(s)
      Masahito Ohta
    • Organizer
      Nagoya Workshop onDifferential Equations
    • Place of Presentation
      名古屋大学
    • Year and Date
      2009-02-03
    • Related Report
      2008 Final Research Report
  • [Presentation] Stability of standingwaves for a system of nonlinearSchrodinger equations with three waveinteraction Workshop"Asymptotics andSingularities in Nonlinear and GeometricDispersive Equations"2008

    • Author(s)
      Masahito Ohta
    • Organizer
      BanffInternational Research Station forMathematical Innovation and Discovery
    • Place of Presentation
      Canada
    • Year and Date
      2008-08-27
    • Related Report
      2008 Final Research Report
  • [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations with three wave interaction2008

    • Author(s)
      Masahito Ohta
    • Organizer
      Nonlinear Wave and Dispersive Equations
    • Place of Presentation
      京都大学
    • Year and Date
      2008-01-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Stability of groundstates for nonlinear Schrodingerequations with nonlocal interaction2007

    • Author(s)
      Masahito Ohta
    • Organizer
      Nonlinear Wave Equations
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-08-29
    • Related Report
      2008 Final Research Report
  • [Presentation] Stability of ground states for nonlinear Schrodinger equations with nonlocal interaction2007

    • Author(s)
      Masahito Ohta
    • Organizer
      Nonlinear Wave Equations
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-08-29
    • Related Report
      2007 Annual Research Report
  • [Presentation] Stability of standing wavesfor nonlinear Schrodinger equationswith a delta function potential2007

    • Author(s)
      太田雅人
    • Organizer
      発展方程式シンポジウム
    • Place of Presentation
      東海大学
    • Year and Date
      2007-03-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Standing waves fornonlinear Schrodinger equations with adelta function potential2006

    • Author(s)
      Masahito Ohta
    • Organizer
      Sapporo GuestHouse Symposium on Mathematics 22," Nonlinear Wave Equations"
    • Place of Presentation
      札幌天神山国際ゲストハウス
    • Year and Date
      2006-11-20
    • Related Report
      2008 Final Research Report
  • [Presentation] Global existence for damped nonlinear Schrodinger equations2006

    • Author(s)
      Masahito Ohta
    • Organizer
      The 6th AIMS International Conference on Dynamical Systems and Differential Equations
    • Place of Presentation
      Universite de Poitiers, France
    • Year and Date
      2006-06-26
    • Related Report
      2008 Final Research Report
  • [Remarks] ホームページ

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/MasahitoOhta.html

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.rimath.Saitama-u.ac.jp/lab.jp/MasahitoOhta.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/MasahitoOhta.html

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi