2003 Fiscal Year Final Research Report Summary
Study on the behavior of solutions in the zero dispersion limit of the nonlinear wave equations with the integral kernel
| Project/Area Number |
14540209
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Yamaguchi University |
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Principal Investigator |
MATSUNO Yoshimasa Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (30190490)
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| 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)
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| Project Period (FY) |
2002 – 2003
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| Keywords | nonlinear wave equation / soliton / modulation theory / zero dispersion limit / inverse scattering method / Benjamin-Ono equation / nonlocal nonlinear Schrodinger equation |
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| 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
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