NONLINEAR SCHR?DINGER EQUATION WITH δ-FUNCTION AS INITIAL DATA

NAOYASU KITA

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NONLINEAR SCHR?DINGER EQUATION WITH δ-FUNCTION AS INITIAL DATA

机译：以δ函数为初始数据的非线性Schr？dinger方程

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摘要

We consider the initial value problem of the nonlinear Schr?dinger equation with superposed δ-functions as initial data. We treat this problem case by case, i.e., the cases in which the initial data consists of single, double and triple δ-functions, respectively. In particular, when the initial data consists of double or triple δ-functions, the solution receives the generation of new modes which is visible only in the nonlinear problem. Furthermore, the solution exists globally in time or blows up in finite time, dependently on the sign of nonlinearity.

机译：我们将叠加了δ函数的非线性薛定ding方程的初值问题视为初始数据。我们逐案处理此问题，即初始数据分别由一个，两个和三个δ函数组成的情况。特别是，当初始数据由双δ函数或三δ函数组成时，解决方案会收到新模式的生成，而新模式仅在非线性问题中可见。此外，取决于非线性的符号，解决方案在时间上全局存在或在有限时间内爆炸。

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《Sugaku expositions: A translation of Sugaku》 |2014年第2期|共19页
作者
NAOYASU KITA;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
NONLINEAR; EQUATION; δ-FUNCTION;

机译：非线性;方程;δ函数;

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机译：L {frown}〜p初始数据具有次临界非线性Schrdinger方程整体解的存在性
2. The Interctitical Defocusing Nonlinear Schr?dinger Equations with Radial Initial Data in Dimensions Four and Higher [J] . Chuanwei Gao, Changxing Miao, Jianwei Yang-Urbain 分析、理论与应用（英文版） . 2019,第002期

机译：径向初始数据为四维或更高维的跨域散焦非线性薛定ding方程
3. The derivation of the conservation law for defocusing nonlinear Schr?dinger equations with non-vanishing initial data at infinity [J] . Hayato Miyazaki Journal of Mathematical Analysis and Applications . 2014,第2期

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4. The trigonometric function transform method and its application for solving coupled nonlinear schrödinger equations [C] . DongBo, LiuXian Pan, Yan JiaRen 2010 International Conference on Computer Application and System Modeling . 2010

机译：三角函数变换方法及其在求解非线性薛定ding方程组中的应用
5. Studies on instability of solitary waves for nonlinear Schr?dinger equations [D] . 深谷　法良 2019

机译：非线性薛定er方程孤波不稳定性的研究
6. Colloquium PaperNonlinear partial differential equations and applications: On the global Cauchy problem for the nonlinear Schrödinger equation [O] . Jean Bourgain 2007

机译：非线性偏微分方程及其应用：关于非线性的整体柯西问题薛定er方程
7. A coupled system of nonlinear Schrödinger equations with delta functions as initial data [O] . Doi Kazuyuki 2008

机译：带有三角函数的非线性Schrödinger方程的耦合系统作为初始数据

NONLINEAR SCHR?DINGER EQUATION WITH δ-FUNCTION AS INITIAL DATA

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