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.我们引入了一种新的相函数，并在求解具有亚临界非线性的非局部非线性薛定谔方程时表现出了渐近行为。这些结果已发表在 Amer.J.Math.1998、SUT J.Math.1998 上。在 Hokkaido 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扩展到具有亚临界幂非线性的局部非线性薛定谔方程。 2.我们研究了时间上的渐近行为通过研究 Airy 函数的性质，J.Funct.Anal.1998 中广义 Korteweg-de Vries 方程的解。我们还在国际数学研究通报，1999.3中证明了修正的Kortweg-de Vries方程的修正散射态的存在性。修正的Beinjamin-Ono是众所周知的非线性色散方程之一。在 Trans.A.M.S.1999 中，我们通过引入新的相位函数证明了修正散射态的存在

项目成果

N. HAYASHI: "Global existence of small solutions to nonlinear Schrodinger equations"J. Non. Anal. T.M.A.. 31. 671-685 (1998)

N. HAYASHI：“非线性薛定谔方程小解的全局存在性”J。

N. HAYASHI: "Asymptotics in Large time of solutions to nonlinear Schrodinger and Hartree. equations"Amer. J. Math.. 120. 369-389 (1998)

N. HAYASHI：“非线性薛定谔和哈特里方程解的大时间渐进”Amer。

N. HAYASHI: "Large time behavior of solutions for the modified Korteweg-de Vries equation"Inter. Math. Research. Notices. 8. 395-418 (1999)

N. HAYASHI：“修正的 Korteweg-de Vries 方程解的大时间行为”Inter。

N. HAYASHI: "Large time behavior of solutions for derivative cubic nonlinear Schrodinger equations"Publ. RIMS, Kyoto Univ.. 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”Publ。

N. HAYASHI: "On Davey-Stewartson and Ishimori systems"Math. Phys., Anal. and Geometry. 2. 53-81 (1999)

N. HAYASHI：“论 Davey-Stewartson 和 Ishimori 系统”数学。