Rogue wave solution for nonlinear evolution equations and its algebraic structure

• Project/Area Number: 26610029
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• 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 神戸大学, 理学研究科, 教授 (80164672)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); 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: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 関数方程式論 / 応用数学

Outline of Final Research Achievements

Rogue wave is a class of solutions for some nonlinear evolution equations which are localized both in time and space. These solutions have rich mathematical structures and describe some interesting phenomena in various physical systems. The theory of integrable systems is applied to investigate the rogue wave solutions for some nonlinear evolution equations. A method to construct general rogue wave solutions is proposed and based on the determinant representation of rogue wave solutions, the algebraic structure of the space of solutions is studied.

Research Products

• [Int'l Joint Research] The University of Texas(米国)
• [Journal Article] Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation (2017)
  • Author(s): Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta
  • Journal Title: Studies in Applied Mathematics Volume: 136 Issue: 3 Pages: 343-367
  • DOI: 10.1111/sapm.12159
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] An integrable semi-discrete Degasperis-Procesi equation (2017)
  • Author(s): B.-F. Feng, K. Maruno and Y. Ohta
  • Journal Title: Nonlinearity Volume: 30 Issue: 6 Pages: 2246-2267
  • DOI: 10.1088/1361-6544/aa67fc
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The Degasperis-Procesi equation, its short wave model and the CKP hierarchy (2017)
  • Author(s): B.-F. Feng, K. Maruno and Y. Ohta
  • Journal Title: Annal. Math. Sci. Appl. Volume: 2 Issue: 2 Pages: 285-316
  • DOI: 10.4310/amsa.2017.v2.n2.a4
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] N-bright-dark soliton solution to a semi-discrete vector nonlinear Schroedinger equation (2017)
  • Author(s): B.-F. Feng and Y. Ohta
  • Journal Title: SIGMA Symmetry Integrability Geom. Methods Appl. Volume: 13 Pages: 071-071
  • DOI: 10.3842/sigma.2017.071
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue (2017)
  • Author(s): B.-F. Feng, K. Maruno and Y. Ohta
  • Journal Title: J. Phys. A: Math. Theor. Volume: 50 Pages: 055201-055201
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] An integrable semi-discretization of the coupled Yajima-Oikawa system (2016)
  • Author(s): J. Chen, Y. Chen, B.-F. Feng, K. Maruno and Y. Ohta
  • Journal Title: J. Phys. A: Math. Theor. Volume: 49 Pages: 165201-165201
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation (2015)
  • Author(s): B.-F. Feng, J. Chen, Y. Chen, K. Maruno and Y. Ohta
  • Journal Title: J. Phys. A: Math. Theor. Volume: 48 Pages: 385202-385202
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] General rogue waves in the focusing and defocusing Ablowitz-Ladik equations (2014)
  • Author(s): Y. Ohta and J. Yang
  • Journal Title: J. Phys. A: Math. Theor. Volume: 47 Pages: 255201-255201
  • Peer Reviewed
• [Presentation] Semi-discrete analogues of the complex short pulse and coupled complex short pulse equations based on the KP hierarchy reduction (2017)
  • Author(s): Baofeng Feng and Yasuhiro Ohta
  • Organizer: AMS Sectional Meeting (Fall Central Sectional Meeting)
  • Int'l Joint Research
• [Presentation] Rogue wave solutions for discrete soliton equations (2016)
  • Author(s): Y. Ohta
  • Organizer: The Fourth International Conference, Nonlinear Waves - Theory and Applications
  • Place of Presentation: Beijing, China
  • Int'l Joint Research / Invited
• [Presentation] Algebraic Solutions of Soliton Equations and Their Applications (2015)
  • Author(s): Y. Ohta
  • Organizer: The 8th International Congress on Industrial and Applied Mathematics
  • Place of Presentation: Beijing, China
  • Year and Date: 2015-08-12
  • Int'l Joint Research / Invited
• [Presentation] Rogue Waves for Some Soliton Equations (2014)
  • Author(s): Y. Ohta
  • Organizer: SIAM Conference on Nonlinear Waves and Coherent Structures
  • Place of Presentation: Cambridge, UK
  • Year and Date: 2014-08-13
  • Invited
• [Presentation] Rogue wave solution of Ablowitz-Ladik equation (2014)
  • Author(s): Y. Ohta
  • Organizer: Symmetries and Integrability in Difference Equations (SIDE 2014)
  • Place of Presentation: Bangalore, India
  • Year and Date: 2014-06-19
  • Invited