On the study of properties of solutions to partial differential equations

偏微分方程解性质的研究

• 批准号: 10640213
• 负责人: HAYASHI Nakao
• 金额: $ 2.11万
• 依托单位: Science University of Tokyo
• 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
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640213/
• 关键词: Schrodinger equations; KdV equations; Benjamin-Ono equations; Nonlinear dissipative eq.; Nonlinear dispersive eq.; Scattering problem; Asymptotics; Analytic functions; シェレディンガー方程式; KP方程式; 解の漸近的ふるまい; 消散型発展方程式

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

1.引入了一种新的相函数，证明了具有亚临界非线性项的非局部非线性Schrodinger方程解的时间渐近性。这些结果发表在Amer.J.Math.1998，SUT J.Math.1998上。在北海道Math. J.1998和Dis.Conti.Dyna.Sys.1999中，我们利用一些解析函数空间将这些结果推广到了具有次临界幂非线性项的局部非线性Schrodinger方程。2.在J.Funct.Anal.1998中，我们利用Airy函数的性质研究了广义Korteweg-de弗里斯方程解的时间渐近性态。在1999年3月的国际数学研究通报中，我们证明了修正的Kortweg-de弗里斯方程的修正散射态的存在性。修正的Beinjamin-Ono方程是著名的非线性色散方程之一。在Trans.A.M.S.1999中，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

项目成果

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。

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。

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。

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)

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。