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.我们引入了一个新的相函数，并在针对具有亚临界非线性的非局部非线性schrodinger方程的解决方案中显示出渐近行为。这些结果已发表在Amer.J.Math.1998，Sut J.Math.1998。在北海道数学。1998年和dis.conti.dyna.sys.1999中，我们将这些结果扩展到具有亚临界功率非线性的本地非线性schrodinger方程，通过使用某些分析功能空间。2。我们通过研究的korteweg-de vries equuntrions.aniguntion.an in witirtion.aniguntion.an in norkity in j.ann in norkity.an in norkity.an in norkity.an in norkity.an in rycuntions.an in norkity.an in norkity.an in rynight.an in norkity.an in norkity.an in ryction。我们还证明了国际数学研究通知中改良的kortweg-de Vries方程的修改散射状态的存在，1999.3.修改的beinjamin-ono被称为众所周知的非线性分散方程之一。在Trans.A.M.S. 1999中，我们通过引入新的相函数展示了修改的散射状态

项目成果

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: "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 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)

N.HAYASHI: "Large time behavior of solutions for derivative cubic nonlinear Schrodinger equations"Pull.RIMS,Kyoto Uniu.. 35. 501-513 (1999)

N.HAYASHI：“导数三次非线性薛定谔方程解的大时间行为”Pull.RIMS，京都大学.. 35. 501-513 (1999)