Study on the asymptotic behavior of solutions for the nonlocal soliton equations in the zero dispersion limit
| Project/Area Number |
16540196
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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) |
MAKINO Tetu Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (00131376)
YANAGI Kenjiro Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (90108267)
KURIYAMA Ken Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (10116717)
NISHIYAMA Takahiro Yamaguchi University, Faculty of Engineering, Associate Professors, 工学部, 助教授 (60333241)
MASUMOTO Makoto Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (50173761)
岡田 真理 山口大学, 工学部, 助教授 (40201389)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2004: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Soliton / Nonlinear wave equation / Zero dispersion limit / Camassa-Holm equation / Degasperis-Procesi equation / Benjamin-Ono equation / Inverse scattering method / Peakon solution |
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| Research Abstract |
1.New representation of the solutions for the nonlocal soliton equations
New representations are obtained for the soliton and peiodic-wave solutions of the Benjamin-Ono and nonlocal nonlinear Schrodinger equations. Their derivation is based on a system of nonlinear algebraic equations. The method used here differs from the corresponding derivation by means of the inverse scattering method.
2.Parametric representation of the multisoliton solution for the Camassa-Holm equation
The multisoliton solution (N-soliton solution) of the Camassa-Holm (CH) equation is constructed by means of the Hodograph transformation. Unlike the usual representation for the soliton solutions, it has a parametric representation. The large time asymptotic of the solution is derived and the formula for the phase shift is obtained.
3.Multisoliton solutions of the Degasperis-Procesi equation and their peakon limit
Using the procedure similar to that used for the CH equation, the one- and two-soliton solutions of the Degaspeis-Procesi (DP) equation are constructed and their properties are explored in detail. A remarkable feature of the one-soliton solution is that the amplitude depends on its velocity nonlinearly. The peakon solution is reduced from the soliton solution by taking the zero dispersion limit. The asymptotic form of the two-soliton solution is also derived together with the associated formula for the phase shift. In a subsequent study, the general N-soliton solution is obtained for the DP equation and its property is examined.
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Report
(3 results)
Research Products
(21 results)
