Extension of universal character and new soliton equations

• Project/Area Number: 19340031
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kobe University
• Principal Investigator: OHTA Yasuhiro Kobe University, 大学院・理学研究科, 准教授 (10213745)
• Co-Investigator(Kenkyū-buntansha): NOUMI Masatoshi 神戸大学, 自然科学系先端融合研究環, 教授 (80164672) ; YAMADA Yasuhiko 神戸大学, 大学院・理学研究科, 教授 (00202383)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥13,650,000 (Direct Cost: ¥10,500,000、Indirect Cost: ¥3,150,000); Fiscal Year 2010: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2009: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2008: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2007: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
• Keywords: 普遍指標 / ソリトン / 可積分系 / 双線形形式 / Camassa-Holm方程式 / 非線形Schrodinger方程式 / 離散KdV方程式 / 戸田格子 / KP理論 / Hankel行列式 / Painleve方程式

Research Abstract

By generalizing the universal charaters, applying reduction and using the direct method of soliton theory, various new soliton equation and their solution are constructed. Some application to mathematical physics physics are also investigated.

Research Products

• [Journal Article] Inte-grable Discretizations for the Short-Wave Model of the Camassa-Holm Equation (2010)
  • Author(s): B.-F.Feng, K.Maruno, Y.Ohta
  • Journal Title: J.Phys.A : Math.Theor. 43 Pages: 265202-265202
  • Peer Reviewed
• [Journal Article] In-tegrable Discretizations of the Short Pulse Equation (2010)
  • Author(s): B.-F.Feng, K.Maruno, Y.Ohta
  • Journal Title: J.Phys.A : Math.Theor 43 Pages: 85203-85203
  • Peer Reviewed
• [Journal Article] Five-Dimensionai AGT Conjecture and the Deformed Vira-soro Algebra (2010)
  • Author(s): H.Awata, Y.Yamada
  • Journal Title: J.High Energy Phys. 1 Pages: 125-125
  • Peer Reviewed
• [Journal Article] Integrable Discretizations for the Short-Wave Model of the Camassa-Holm Equation (2010)
  • Author(s): B.-F.Feng, et al.
  • Journal Title: J.Phys.A : Math.Theor. Volume: 43 Pages: 265202-265202
  • Peer Reviewed
• [Journal Article] Integrable Discretizations of the Short Pulse Equation (2010)
  • Author(s): B.-F.Feng
  • Journal Title: J.Phys.A : Math.Theor. Volume: 43 Pages: 85203-85203
  • Peer Reviewed
• [Journal Article] Bilinearization and Casorati Determinant Solutions to Non-autonomous 1+1 Dimensional Discrete Soli- ton Equations (2009)
  • Author(s): K.Kajiwara, Y.Ohta
  • Journal Title: RIMS Kokyuroku Bessatsu B13 Pages: 53-73
  • Peer Reviewed
• [Journal Article] Discretization of Coupled Non-linear Schrodinger Equations (2009)
  • Author(s): Y.Ohta
  • Journal Title: Stud.Appl.Math 122 Pages: 427-447
  • Peer Reviewed
• [Journal Article] Note on the Two-Component Analogue of Two- Dimensional Long Wave-Short Wave Reso-nance Interaction System (2009)
  • Author(s): K.Maruno, Y.Ohta, M.Oikawa
  • Journal Title: Glasgow Math.J. 51A Pages: 129-135
  • Peer Reviewed
• [Journal Article] Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications, Symmetry Integrability Geom. (2009)
  • Author(s): Y.Komori, M.Noumi, J.Shiraishi
  • Journal Title: Methods Appl 5 Pages: 54-54
  • Peer Reviewed
• [Journal Article] A Lax Formalism for the El-liptic Difference Painleve Equation, Sym-metry Integrability Geom (2009)
  • Author(s): Y.Yamada
  • Journal Title: Methods Appl 5 Pages: 42-42
  • Peer Reviewed
• [Journal Article] Padc Method to Painlevc Equations (2009)
  • Author(s): Y.Yamada
  • Journal Title: Funkcial.Ekvac 52 Pages: 83-92
  • Peer Reviewed
• [Journal Article] Bilinearization and Casorati Determinant Solutions to Non-autonomous 1+1 Dimensional Discrete Soliton Equations (2009)
  • Author(s): K. Kajiwara, Y. Ohta
  • Journal Title: RIMS Kokyuroku Bessatsu B13 Pages: 53-73
  • Peer Reviewed
• [Journal Article] Discretization of Coupled Nonlinear Schrodinger Equations (2009)
  • Author(s): Y. Ohta
  • Journal Title: Stud. Appl. Math. 122 Pages: 427-447
  • Peer Reviewed
• [Journal Article] Note on the Two-Component Analogue of Two-Dimensional Long Wave-Short Wave, Resonance Interaction System (2009)
  • Author(s): K. Maruno, Y. Ohta, M. Oikawa
  • Journal Title: Glasgow Math. J. 51A Pages: 129-135
  • Peer Reviewed
• [Journal Article] Bilinearization and Casorati Determinant Solutions to Non-autonomous 1+1 Dimensional Discrete Soliton Equations (2009)
  • Author(s): K.Kajiwara, et al.
  • Journal Title: RIMS Kokyuroku Bessatsu B13 Pages: 53-73
  • Peer Reviewed
• [Journal Article] Discretization of Coupled Nonlinear Schrodinger Equations (2009)
  • Author(s): Y.Ohta
  • Journal Title: Stud.Appl.Math. 122 Pages: 427-447
  • Peer Reviewed
• [Journal Article] Note on the Two-Component Analogue of Two-Dimensional Long Wave-Short Wave Resonance Interaction System (2009)
  • Author(s): K.Maruno, et al.
  • Journal Title: Glasgow Math.J. 51A Pages: 129-135
  • Peer Reviewed
• [Journal Article] An Integrable Semi-Discretization of the Camassa-Holm Equation and Its Determinant Solu-tion (2008)
  • Author(s): Y.Ohta, K.Maruno, B.-F.Feng
  • Journal Title: J.Phys.A: Math.Theor 41 Pages: 355205-355205
  • Peer Reviewed
• [Journal Article] Localized Soli-tons of a (2+1)-Dimensional Nonlocal Non- linear Schrodinger Equation (2008)
  • Author(s): K.Maruno, Y.Ohta
  • Journal Title: Phys.Lett.A 372 Pages: 4446-4450
  • Peer Reviewed
• [Journal Article] Bilinearization and Casorati Determinant Solution to the Non-Autonomous Discrete KdV Equation (2008)
  • Author(s): K.Kajiwara, Y.Ohta
  • Journal Title: J.Phys.Soc.Jpn 77 Pages: 54004-54004
  • NAID: 110006665992
  • Peer Reviewed
• [Journal Article] Bilinearization and Casorati determinant solution to the non-autonomous discrete KdV equation (2008)
  • Author(s): K. Kajiwara, Y. Ohta
  • Journal Title: J. Phys. Soc. Jpn. 77 Pages: 54004-54004
  • NAID: 110006665992
  • Peer Reviewed
• [Journal Article] An integrable semi-discretization of the Camassa-Holm equation and itsdeterminant solution (2008)
  • Author(s): Y. Ohta, et al.
  • Journal Title: J. Phys. A 41 Pages: 355205-355205
  • Peer Reviewed
• [Journal Article] Localized solitons of a (2+l)-dimensional nonlocal nonlinear Schrodingerequation (2008)
  • Author(s): K. Maruno, et al.
  • Journal Title: Phys. Lett. A 372 Pages: 4446-4450
  • Peer Reviewed
• [Journal Article] Bilinearization and Casorati determinant solution to the non-autonomous discrete KdV equation (2008)
  • Author(s): K. Kajiwara, et al.
  • Journal Title: J. Phys. Soc. Jpn. 77 Pages: 54004-54004
  • Peer Reviewed
• [Journal Article] A Renxark on the Hankel Determinant For-mula for Solutions of the Toda Equation (2007)
  • Author(s): K.Kajiwara,M.Ma,zzocco, Y.Ohta
  • Journal Title: J.Phys.AlMath.Theor 40 Pages: 12661-12675
  • Peer Reviewed
• [Journal Article] Quasideterminant Solutions of a Non-Abelian Hirota-Miwa Equation (2007)
  • Author(s): C.R.Gilson,J.J.C.Nilnlnoa, Y.Ohta
  • Journal Title: J.Phys.A : Math Theor. 40 Pages: 12607-12617
  • Peer Reviewed
• [Journal Article] Tau Functions in Combinatorial Bethe Ansatz (2007)
  • Author(s): A.Kuniba, R.Sakamoto, Y.Yamada
  • Journal Title: Nuclear Phys.B 786 Pages: 207-266
  • Peer Reviewed
• [Journal Article] A remark on the Hankel determinant formula for solutions of the Toda equation (2007)
  • Author(s): K. Kajiwara, et. al.
  • Journal Title: J. Phys. A 40 Pages: 12661-12675
  • Peer Reviewed
• [Journal Article] Quasideterminant solutions of a non-abelian Hirota-Miwa equation (2007)
  • Author(s): C. R. Gilson, et. al.
  • Journal Title: J. Phys. A 40 Pages: 12607-12617
  • Peer Reviewed
• [Presentation] Dark and bright soliton solutions for coupled derivative nonlinear Schrodinger equation (2011)
  • Author(s): Y.Ohta
  • Organizer: Dark and bright soliton solutions for coupled derivative nonlinear Schrodinger equation
  • Place of Presentation: New Orleans, USA
  • Year and Date: 2011-01-06
• [Presentation] Dark and bright soliton solutions for coupled derivative nonlinear Schrodinger equation (2011)
  • Author(s): Y.Ohta
  • Organizer: 2011 Joint Mathematics Meetings
  • Place of Presentation: New Orleans, USA
  • Year and Date: 2011-01-06
• [Presentation] Coordinate transformation and discretization for soliton equation (2010)
  • Author(s): Y.Ohta
  • Organizer: GCOE conference : Algebraic and geometric as-pects of discrete integrable systems In-tegrable systems and cluster algebras
  • Place of Presentation: Tokyo, Japan
  • Year and Date: 2010-12-15
• [Presentation] Discrete sine-Gordon equations : hyperbolic and elliptic types (2010)
  • Author(s): Y.Ohta
  • Organizer: Symmetry Plus Integrability 2010
  • Place of Presentation: South Padre Island, USA.
  • Year and Date: 2010-06-14
• [Presentation] Determinant identities arising from soliton theory (2010)
  • Author(s): Y.Ohta
  • Organizer: China-Japan Joint Work-shop on Integrable Systems
  • Place of Presentation: Shaoxing, China
  • Year and Date: 2010-01-09
• [Presentation] Dark soliton solution of Sasa-Satsuma equation (2009)
  • Author(s): Y.Ohta
  • Organizer: International Workshop on Non-linear and Modern Mathematical Physics
  • Place of Presentation: Beijing, China
  • Year and Date: 2009-07-20
• [Presentation] Dark soliton solution of Sasa-Satsuma equation (2009)
  • Author(s): Y. Ohta
  • Organizer: International Workshop on Nonlinear and Modern Mathematical Physics
  • Place of Presentation: Beijing, China
  • Year and Date: 2009-07-20
• [Presentation] Discretization of coupled nonlin-ear Schrodinger equations (2008)
  • Author(s): Y.Ohta
  • Organizer: International Co i-ference : Nonlinear Waves Theory and Ap-plications
  • Place of Presentation: Beijing, China
  • Year and Date: 2008-07-09
• [Presentation] Backlund transformation of Toda lattice and solution of Painleve equation (2008)
  • Author(s): Y.Ohta
  • Organizer: 8th International Conference on Synune-tries and Integrability of Difference Equa-tions
  • Place of Presentation: Montreal, Canada
  • Year and Date: 2008-06-23
• [Presentation] Backlund transformation of Toda lattice and solution of Painleve equation (2008)
  • Author(s): Y. Ohta
  • Organizer: 8th International Conference on Symmetries and Integrability of Difference Equations
  • Place of Presentation: Montreal (カナダ)
  • Year and Date: 2008-06-23
• [Presentation] Vec-tor soliton and multi-component KP hier-archy (2008)
  • Author(s): K.Maruno, Y.Ohta, M.Oikawa
  • Organizer: AMS Joint Mathematics Meetings
  • Place of Presentation: San Diego, USA
  • Year and Date: 2008-01-09
• [Presentation] Vector soliton and multi-component KP hierarchy (2008)
  • Author(s): K. Maruno, et. al.
  • Organizer: AMS Joint Mathematics Meetings
  • Place of Presentation: San Diego, USA
  • Year and Date: 2008-01-09
• [Presentation] 離散戸田格子方程式と直交多項式系 (2007)
  • Author(s): 太田泰広
  • Organizer: 研究集会「ソリトンの数理とその応用:非線形波動から可積分系へ」
  • Place of Presentation: 山口,日本
  • Year and Date: 2007-12-23