| Project/Area Number |
10640213
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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 | Science University of Tokyo |
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Principal Investigator |
HAYASHI Nakao Science Univ.of Tokyo, Faculty of Sience, Professor, 理学部, 教授 (30173016)
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| Co-Investigator(Kenkyū-buntansha) |
UNAI Akihito Science Univ.of Tokyo, Faculty of Sience, Associate Professor, 理学部, 助手 (50297610)
OGASAWARA Hideko Science Univ.of Tokyo, Faculty of Sience, Associate Professor, 理学部, 助手 (00231217)
KATO Keiichi Science Univ.of Tokyo, Faculty of Sience, Associate Professor, 理学部, 講師 (50224499)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Schrodinger equations / KdV equations / Benjamin-Ono equations / Nonlinear dissipative eq. / Nonlinear dispersive eq. / Scattering problem / Asymptotics / Analytic functions |
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| Research Abstract |
1.We introduced a new phase function and showed asymptotic behavior in time of solutions to nonlocal nonlinear Schrodinger equations with sub-critical nonlinearities. These results have been published in Amer.J.Math.1998, SUT J.Math.1998. In Hokkaido Math .J.1998 and Dis.Conti.Dyna.Sys.1999 we extended these results to local nonlinear Schrodinger equations with sub-critical power nonlinearities by making use of some analytic function spaces.
2.We studied asymptotic behavior in time of solutions to generalized Korteweg-de Vries equations in J.Funct.Anal.1998 by investigating the property of Airy function. We also proved the existence of the modified scattering states of modified Kortweg-de Vries equation in International Mathematics Research Notices, 1999.
3.Modified Beinjamin-Ono is known as one of the well known nonlinear dispersive equations. In Trans.A.M.S.1999 we showed the existence of modified scattering states by introducing a new phase function
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