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Study on the behavior of solutions in the zero dispersion limit of the nonlinear wave equations with the integral kernel

Research Project

Project/Area Number 14540209
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionYamaguchi University

Principal Investigator

MATSUNO Yoshimasa  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (30190490)

Co-Investigator(Kenkyū-buntansha) KURIYAMA Ken  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (10116717)
YANAGI Kenjiro  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (90108267)
MAKINO Tetu  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (00131376)
MASUMOTO Makoto  Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (50173761)
OKADA Mari  Yamaguchi University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40201389)
柳原 宏  山口大学, 工学部, 助教授 (30200538)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywordsnonlinear wave equation / soliton / modulation theory / zero dispersion limit / inverse scattering method / Benjamin-Ono equation / nonlocal nonlinear Schrodinger equation
Research Abstract

1. Exactly solvable eigenvalue problem
The linear eigenvalue problem is solved for the nonlocal nolonear Schrodinger (NLS) equation in the context of the inverse scattering method when the potential is the multisolison solution
2. Relation to exactly solvable dynamical systems
The motion of poles of the soliton and periodic solutions of the nonlocal NLS equation is investigated from the viewpoint of the dynamical system in the complex plane
3. Modulation theory
The modulation problem is analyzed for the periodic solution of the nonlocal NLS equation. The modulation equations for the wave parameters are derived and they are solved explicitly
4. Formulation of the initial value problem
The initial value problem of the nonlocal NLS equation is formulated by means of the inverse scattering transform method. A system of equations are derived for the Jost functions
5. New formula for the soliton solution
The multisoliton solution of the Benjamin-Ono equation is derived from a system of nonlinear algebraic equations. This result is a new finding which is never anticipated from the scheme of the inverse scattering method

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] Y.Matsuno: "A Cauchy problem for the nonlocal nonlinear Schrodinger equation"Inverse Problems. 20. 437-445 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "A system of nonlinear algebraic equations connected with the multisoliton solution of the Benjamin-Ono equation"Journal of Mathematical Physics. 45. 795-802 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Asymptotic solutions of the nonlocal nonlinear Schrodinger equation in the limit of small dispersion"Physics Letters A. 309(1-2). 83-89 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Exactly solvable eigenvalue problem for a nonlocal nonlinear Schrodinger equation"Inverse Problems. 18. 1101-1125 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Calogero-Moser Sutherland dynamical systems associated with nonlocal nonlinear Schrodinger equation for envelop waves"Journal of the Physical Society of Japan. 71(6). 1415-1418 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Makino: "Approximations of relativistic Euler-Poisson-Darboux equation"Funkcialaj Ekvacioj. 46. 23-45 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Recent Topics on a Class of Nonlinear Integrodifferential Evolution Equations of Physical Significance, in Advances in Mathematics Research Vol.4"Nova Science, New York. 71 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "A Cauchy problem for the nonlocal nonlinear Schrodinger equation"Inverse Problems. Vol.20. 437-445 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "A system of nonlinear algebraic equations connected with the multisoliton solution of the Benjamin-Ono equation"Journal of Mathematical Physics. Vol.45. 795-802 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Asymptotic solutions of the nonlocal nonlinear Schrodinger equation in the limit of small dispersion"Physics Letters A. Vol.309. 83-89 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Exactly solvable eigenvalue problem for a nonlocal nonlinear Schrodinger equation"Inverse Problems. Vol.18. 1101-1125 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Calogero-Moser-Sutherland dynamical systems associated with nonlocal nonlinear Schrodinger equation For envelop waves"Journal of the Physical Society of Japan. Vol.71. 1415-1418 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Makino: "Approximations of relativistic Euler-Poisson-Darboux equation"Funkcialaj Ekvacioj. Vol.46. 23-45 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "Recent Topics on a Class of Nonlinear Integrodifferential Evolution Equations of Physical Significance"Advances in Mathematics Research, Edited by G. Oyibo, Nova Science. Vol.4. 19-89 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuno: "A Cauchy problem for the nonlocal nonlinear Schrodinger equation"Inverse Problems. 20. 437-445 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Matsuno: "A system of nonilear algebraic equation connected with the multisoliton solution of the Benjamin-Ono equation"Journal of Mathematical Physics. 45. 795-802 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Makino: "Approximation of he Relativistic Euler-Poisson-Darboux Equation"Funkcialaj Ekvacioj. 46. 23-45 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] C.-H.Hsu, T.Makino: "Spherically symmetric solutions to the compressible Euler equation with An asymptotic γ-law"Japan Journal of Industrial and Applied Mathematics. 20. 1-15 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Furuichi, K.Yanagi, K.Kuriyama: "A sufficient condition on concavity of the auxiliary function appearingin quantum reliability function"INFORMATION. 6. 71-76 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Okada: "Free boundary problem for one-dimensional motion of compressible gas with density-dependent viscosity and vacuum"Japan Journal of Industrial and Applied Mathematics. 20(発表予定). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Matsuno: "Recent Topics on a class of Integrodifferential Evolution Equations of Physical Significance, in Advances in Mathematics Research Vol.4"Nova Science. 71 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Matsuno: "Calogero-Moser-Sutherland dynamical systems associated with nonlocal nonlinear Schrodinger equation for envelope waves"Journal of the Physical Society of Japan. 71(6). 1515-1518 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Matsuno: "Exactly solvable eigenvalue problem for a nonlocal nonlinear Schrodinger equation"Inverse Problems. 18. 1101-1125 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Matsuno: "Asymptotic solutions of the nonlocal nonlinear Schrodmger equation in the limit of small dispersion"Physics Letters A. 309(1-2). 83-89 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Makino: "Approximations of the relativistic Euler-Poisson-Darboux equation"Funkcialaj Ekvacioj. 46(1)(発表予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Okada: "Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity"Ann. Univ. Rerrara Sez. VII-Sc. Mat.. XLVIII. 1-20 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Masumoto: "Hyperbolically maximal domains and fundamental domains for a discontinuous group of conformal automorphisms of a Riemann surface"The Quarterly Journal of Mathematics. 53(3). 337-346 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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