Analysis of standing waves for nonlinear Schroedinger equations with harmonic potential

• Project/Area Number: 26800074
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Tsuda College
• Principal Investigator: Hiroaki Kikuchi 津田塾大学, 学芸学部, 准教授 (00612277)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 非線形シュレディンガー方程式 / 基底状態 / 散乱解 / 爆発解 / 一般化リュウビル・ゲルファンド方程式 / 特異解 / 分岐 / モース指数 / 大域挙動 / 散乱 / 爆発 / 定在波 / ビリアル恒等式 / 一意性 / 一般化リュウビル・ゲルファント問題 / エネルギー臨界 / 質量臨界 / リウビル・ゲルファント問題 / 折れ曲がり

Outline of Final Research Achievements

First result I obtained is concerned with the global dynamics of solutions to nonlinear Schrodinger equations. Second one is to study a bifurcation diagram of generalized Liouville-Gelfand equations.

Research Products

• [Int'l Joint Research] University of British Columbia(Canada)
• [Journal Article] Bifurcation diagram of solutions to elliptic equation with exponential nonlinearity in higher dimensions (2017)
  • Author(s): Hiroaki Kikuchi
  • Journal Title: Proceedings of the Royal Society of Edinburgh Section A: Mathematics Volume: 印刷中
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Global dynamics above the ground state energy for a class of nonlinear Schrodinger equations with critical growth (2017)
  • Author(s): Hiroaki Kikuchi
  • Organizer: THE TENTH IMACS INTERNATIONAL CONFERENCE ON NONLINEAR EVOLUTION EQUATIONS AND WAVE PHENOMENA: COMPUTATION AND THEORY
  • Place of Presentation: University of Georgia
  • Int'l Joint Research / Invited
• [Presentation] Global dynamics above the ground state energy for the combined power-type nonlinear Schrodinger equations with energy-critical growth at low frequencies (2016)
  • Author(s): 菊池弘明
  • Organizer: 北海道大学PDE seminar
  • Place of Presentation: 北海道大学
  • Invited
• [Presentation] Asymptotic behavior of solutions for a class of nonlinear Schr\"odinger equations (2016)
  • Author(s): Hiroaki Kikuchi
  • Organizer: AIMS Conference 2016
  • Place of Presentation: Orland
  • Int'l Joint Research / Invited
• [Presentation] 指数型非線形項をもつ楕円型方程式の正値解の分岐について (2016)
  • Author(s): 菊池弘明
  • Organizer: NLPDE セミナー
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] 指数型非線形項をもつ楕円型方程式の正値解の分岐ダイアグラム (2016)
  • Author(s): 菊池弘明
  • Organizer: 応用数学セミナー
  • Place of Presentation: 東北大学
  • Invited
• [Remarks] 研究代表者のホームページ
  • URL: http://edu.tsuda.ac.jp/~hiroaki/
• [Remarks] 研究代表者のホームページ
  • URL: http://edu.tsuda.ac.jp/~hiroaki/index.html