On the study of properties of solutions to partial differential equations
On the study of properties of solutions to partial differential equations
批准号:
10640213
负责人:
HAYASHI Nakao
金额:
$2.11万
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
1998
资助国家:
日本
项目状态:
已结题
起止时间:
1998 至 1999
中文摘要
1.我们引入了一个新的相函数,并证明了具有亚临界非线性的非局部非线性薛定谔方程解在时间上的渐近性。这些结果发表在《Amer.J.Math》杂志上。1998,中山大学数学研究所。在北海道数学。1998年,dis . con . dyna . sys。利用解析函数空间,将这些结果推广到具有亚临界幂非线性的局部非线性薛定谔方程。研究了广义Korteweg-de Vries方程解在时间上的渐近行为。1998年通过研究Airy函数的性质。我们也在《国际数学研究通报》1999.3中证明了修正Kortweg-de Vries方程修正散射态的存在性。修正Beinjamin-Ono方程是众所周知的非线性色散方程之一。在Trans.A.M.S。1999年我们通过引入一个新的相函数证明了修正散射态的存在性
英文摘要
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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N. HAYASHI: "On the scattering theory for the cubic nonlinear Schrodinger and Hartree type equations in one space dimension"Hokkaido Math. J.. 27. 651-667 (1998)
N. HAYASHI:“关于一维空间中三次非线性薛定谔和哈特里型方程的散射理论”北海道数学。
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N. HAYASHI: "Large time behavior of solutions for derivative cubic nonlinear Schrodinger equations without a self-conjugate property"Funk cialaj Ekvacioj. 42. 311-324 (1999)
N. HAYASHI:“没有自共轭性质的导数三次非线性薛定谔方程解的大时间行为”Funk cialaj Ekvacioj。
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N.Hayashi, P.I.Naumkin and P.N.Pipolo: "Smoothing effects for some derivative nonlinear Schrodinger equations"Discrete and Continuous Dynamical Systems. 5. 685-695 (1999)
N.Hayashi、P.I.Naumkin 和 P.N.Pipolo:“某些导数非线性薛定谔方程的平滑效应”离散和连续动力系统。
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N.Hayashi and P.I.Naumkin and H.Uchida: "Large time behavior of solutions for derivative cubic nonlinear Schrodinger equations"Publ.RIMS, Kyoto Univ.. 35. 501-513 (1999)
N.Hayashi 和 P.I.Naumkin 和 H.Uchida:“导数三次非线性薛定谔方程解的大时间行为”Publ.RIMS,京都大学.. 35. 501-513 (1999)
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A.de Bouard: "Scattering problem and asymptotics for a relativistic nonlinear Schrodinger equation"Nonlinearity. 12. 1415-1425 (1999)
A.de Bouard:“相对论非线性薛定谔方程的散射问题和渐进问题”非线性。
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共 54 条
Asymptotic analysis for systems of dispersive equations
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批准号:24654034
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项目类别:Grant-in-Aid for Challenging Exploratory Research
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资助金额:$1.25万
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财政年份:2012
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负责人:HAYASHI Nakao
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依托单位:
On study of evolution equations with hyperbolic properties
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批准号:19340030
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项目类别:Grant-in-Aid for Scientific Research (B)
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资助金额:$8.32万
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财政年份:2007
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负责人:HAYASHI Nakao
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依托单位:
On study of partial differential equations describing natural phenomena
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批准号:15204009
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项目类别:Grant-in-Aid for Scientific Research (A)
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资助金额:$13.64万
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财政年份:2003
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负责人:HAYASHI Nakao
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依托单位:
ON SOLUTIONS OF NONLINEAR DISPERSIVE EQUATIONS
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批准号:12440050
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项目类别:Grant-in-Aid for Scientific Research (B)
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资助金额:$5.82万
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财政年份:2000
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负责人:HAYASHI Nakao
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依托单位: