Singular limit of tau function for soliton equations and its application

• Project/Area Number: 18H01130
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Kobe University
• Principal Investigator: Ohta Yasuhiro 神戸大学, 理学研究科, 教授 (10213745)
• Co-Investigator(Kenkyū-buntansha): 山田 泰彦 神戸大学, 理学研究科, 教授 (00202383) ; 野海 正俊 立教大学, 理学研究科, 特任教授 (80164672)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2023)
• Budget Amount: ¥15,730,000 (Direct Cost: ¥12,100,000、Indirect Cost: ¥3,630,000); Fiscal Year 2022: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2021: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2020: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2019: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2018: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
• Keywords: 函数方程式論

Outline of Final Research Achievements

In nonlinear integrable evolution equations, it is possible to derive new system of equations and their solutions by taking a kind of singular limit. Based on the bilinear method in the theory of integrable systems, the way to construct solutions in the limit is proposed, and the algebraic structure of the systems and the analytic properties of the solutions are investigated.

Academic Significance and Societal Importance of the Research Achievements

古典可積分系のＫＰ系列の理論においては、広いクラスの方程式系を構成、分類して、その解空間の代数構造を明らかにすることは、理論応用両面において重要である。本研究では、連続系離散系の両者を対象として、局在構造や特異点構造などの新しい構造をもつ解を具体的に構成することによって、ある種の特異性のある極限をとることによって初めて現れる方程式系およびその解に関する研究を進展させた。

Research Products

• [Journal Article] General rogue wave solution to the discrete nonlinear Schr\"odinger equation (2022)
  • Author(s): Yasuhiro Ohta and Bao-Feng Feng
  • Journal Title: Phys. D Volume: 439 Pages: 133400
  • DOI: 10.1016/j.physd.2022.133400
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Discrete local induction equation (2019)
  • Author(s): S. Hirose, J. Inoguchi, K. Kajiwara, N. Matsuura and Y. Ohta
  • Journal Title: J. Integrable Syst. Volume: 3 Pages: xyz003
  • Peer Reviewed
• [Journal Article] Isoperimetric deformations of curves on the Minkowski plane (2019)
  • Author(s): H. Park, J. Inoguchi, K. Kajiwara, K. Maruno, N. Matsuura and Y. Ohta
  • Journal Title: Int. J. Geom. Methods Mod. Phys. Volume: 16 Pages: 1950100
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Discrete and ultradiscrete periodic phase soliton equations (2019)
  • Author(s): H. Nagai, Y. Ohta and R. Hirota
  • Journal Title: J. Phys. Soc. Jpn. Volume: 88 Pages: 034001
  • Peer Reviewed
• [Journal Article] The derivative Yajima-Oikawa system: bright, dark soliton and breather solutions (2018)
  • Author(s): J. Chen, B.-F. Feng, K. Maruno and Y. Ohta
  • Journal Title: Stud. Appl. Math. Volume: 141 Pages: 145-185
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Determinant formula for Rogue waves and the binomial theorem (2023)
  • Author(s): Yasuhiro Ohta
  • Organizer: 10th International Congress on Industrial and Applied Mathematics
  • Int'l Joint Research / Invited
• [Presentation] Rogue wave に関する最近の話題 (2023)
  • Author(s): 太田 泰広
  • Organizer: RIMS共同研究（公開型） 可積分系数理における最近の展開
  • Invited
• [Presentation] On Airy function type solutions of KP equation (2023)
  • Author(s): Yasuhiro Ohta
  • Organizer: Workshop on Nonlinear Water Waves and Related Topics
  • Int'l Joint Research / Invited
• [Presentation] Interaction of rogue waves (2022)
  • Author(s): Y. Ohta
  • Organizer: International Workshop on Rogue Waves
  • Int'l Joint Research / Invited
• [Presentation] 一般的な境界条件での自己適合移動格子スキームと数値計算 (2021)
  • Author(s): 丸野健一, 太田泰広
  • Organizer: 日本物理学会
• [Presentation] Discretization of the Liouville equation of elliptic type (2019)
  • Author(s): Y. Ohta
  • Organizer: The 2nd JNMP Conference on Nonlinear Mathematical Physics: 2019
  • Int'l Joint Research / Invited
• [Presentation] Dark soliton solutions for toroidal type soliton equations (2019)
  • Author(s): Y. Ohta
  • Organizer: ISLAND V: Integrable systems, special functions and combinatorics
  • Int'l Joint Research / Invited
• [Presentation] An expression of lambda determinant derived from Toda lattice equation (2019)
  • Author(s): Y. Ohta
  • Organizer: The 9th International Congress on Industrial and Applied Mathematics
  • Int'l Joint Research / Invited
• [Presentation] Two dimensional stationary vorticity distribution and integrable system (2019)
  • Author(s): Y. Ohta
  • Organizer: The Eleventh IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory
  • Int'l Joint Research / Invited
• [Presentation] Periodic phase solitons for discrete and ultradiscrete equations (2018)
  • Author(s): Y. Ohta
  • Organizer: Scientific Gathering, Integrable systems and beyond
  • Int'l Joint Research / Invited