ON SOLUTIONS OF NONLINEAR DISPERSIVE EQUATIONS

关于非线性色散方程的解

• 批准号: 12440050
• 负责人: HAYASHI Nakao
• 金额: $ 5.82万
• 依托单位: Osaka University (2001-2002)Tokyo University of Science (2000)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12440050/
• 关键词: Schredinger equation; Modified KdV equation; Scattering problem; Asymptotics of solutions; KdV-Burgers equation; Landau-Ginzburg type equation; boundary value problem; KdV equation on a halfline; シュ・レデインガー方程式; 非線形分散型方程式; Schredinger equation; Modified KdV equation; Scattering problem; Asymptotics of solutions; KdV-Burgers equation; Landau-Ginzburg type equation; boundary value problem; KdV equation on a halfline; シュ・レデインガー方程式; 非線形分散型方程式

1. P.I. Naumkin and I studied asymptotic behavior of solutions to one dimensional nonlinear Schredinger equations with cubic nonlinearities. In this project we showed properties of solutions strongly depend on structures of nonlinearities and angular part of the data.2. E.I. Kaikina and I studied asymptotic behavior of solutions to various dissipative nonlinear equations on the positive half line. We made use of the facts that solutions have better time decay by refrection at the boundary compared to the problem in the full.3. P.I. Naumkin and I studied asymptotic and scattering problems of two dimensional nonlinear Schredinger equations with quadratic nonlinearities involving derivatives of the unknown function. In this work we used some analytic function space to get a sufficient time decay of solutions to get the desired result.4. P.I. Naumkin, H.Uchida and I studied the elliptic-hyperbolic Davey-Stwertson system and showed an analytical smoothing property of solutions when the data decay exponentially at infinity. We made use of the nonlinearity satisfies the gauge invariant and the operator which commute with the Schredinger operator.5. P.I. Naumkin and I studied asymptotic behavior of solutions to one dimensional nonlinear Schredinger equations with quadratic nonlinearities. We used the normal form method to translate the equation to another one which-has cubic nonlinearities and applied the previous method stated in (1).6. E.I. Kaikina, P.I. Naumkin and I studied complex Landau-Ginzburg equations with critical nonliaearities and showed asymptotics of solutions by using third approximation of solutions and nonlinear transformation.

1。P.I。我和Naumkin研究了解决方案的渐近行为对具有立方非线性的一维非线性Schredinger方程。在这个项目中，我们显示了溶液的特性在很大程度上取决于非线性的结构和数据的角部分。2。 E.I.凯基纳和我研究了正线上各种耗散非线性方程的溶液的渐近行为。我们利用了以下事实，即与全部问题相比，解决方案在边界的反思上具有更好的时间衰减。3。 P.I. Naumkin和我研究了具有二维非线性Schredinger方程的渐近和散射问题，具有二次非线性，涉及未知功能的衍生物。在这项工作中，我们使用了一些分析功能空间来获得足够的解决方案的时间衰减以获得所需的结果4。 P.I. Naumkin，H.uchida和我研究了椭圆形的Hyperbolic Davey-Stwertson系统，当数据衰减在无穷大时呈指数衰减时，溶液的分析平滑性能。我们利用非线性满足了与Schredinger操作员上下班的量规不变的量规。5。 P.I. Naumkin和我研究了溶液对具有二次非线性的一维非线性Schredinger方程的渐近行为。我们使用正常形式的方法将方程式转换为另一种方程，该方程是三次非线性的，并应用了（1）.6中所述的先前方法。 E.I. Kaikina，P.I。 Naumkin和我研究了具有关键非核心的复杂Landau-Ginzburg方程，并通过使用第三次近似溶液和非线性转化来显示溶液的渐近液。