二维线性色散方程的色散量子化现象

尹子涵; 康静

doi:10.21656/1000-0887.410142

二维线性色散方程的色散量子化现象

doi: 10.21656/1000-0887.410142

尹子涵¹,
康静^2, ,

1. 宁波大学数学与统计学院，浙江宁波 315211;
2. 西北大学数学学院，西安 710127

基金项目:

国家自然科学基金(11631007；11871395)

详细信息

作者简介:
尹子涵(1995—)，男，硕士(E-mail: 952917734@qq.com)；康静(1979—)，女，教授(通讯作者. E-mail: jingkang@nwu.edu.cn).

通讯作者:
康静(1979—)，女，教授(通讯作者. E-mail: jingkang@nwu.edu.cn).

中图分类号: O29
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- 被引次数: 0
出版历程
- 收稿日期: 2020-05-19
- 修回日期: 2020-05-23

Dispersive Quantization of 2D Linear Dispersive Equations

YIN Zihan¹,
KANG Jing^{2
, ,}

1. School of Mathematics and Statistics, Ningbo University,Ningbo, Zhejiang 315211, P.R.China;
2. School of Mathematics, Northwest University, Xi’an 710127, P.R.China

Funds:

The National Natural Science Foundation of China(11631007；11871395)

摘要

摘要: 研究了定义在平面有界矩形区域的二维线性KdV方程和二维线性Schrödinger方程的色散量子化现象.证明了在有理时刻，方程周期初边值问题的解是初值条件的线性组合，而在无理时刻，解呈现类分形，连续不可微的状态.
- 二维线性KdV方程 /
- 色散量子化 /
- 初边值问题 /
- Fourier级数 /
- 二维线性Schröinger方程
Abstract: The dispersive quantization of the 2D linear KdV equation and the 2D linear Schrödinger equation were studied over a bounded rectangle domain in the plane. The research shows that, for the KdV equation, if the period ratio is a rational number, at the rational moments, the solution to the periodic initial boundary value problem will be the linear combination of the initial value conditions; whereas, at the irrational moments, the solution will be continuous and nondifferentiable, and exhibit a fractallike profile. The same is true for the 2D linear Schrödinger equation.
- 2D linear KdV equation /
- dispersive quantization /
- initial boundary value problem /
- Fourier series /
- 2D linear Schrdinger equation

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参考文献(19)

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