Dispersive Quantization of 2D Linear Dispersive Equations
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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.
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关键词:
- 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 fractallike profile. The same is true for the 2D linear Schrödinger equation. -
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