Dispersive Quantization of 2D Linear Dispersive Equations

YIN Zihan; KANG Jing

doi:10.21656/1000-0887.410142

Volume 42 Issue 7

Jul. 2021

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YIN Zihan, KANG Jing. Dispersive Quantization of 2D Linear Dispersive Equations[J]. Applied Mathematics and Mechanics, 2021, 42(7): 741-750. doi: 10.21656/1000-0887.410142

Citation:

YIN Zihan, KANG Jing. Dispersive Quantization of 2D Linear Dispersive Equations[J]. Applied Mathematics and Mechanics, 2021, 42(7): 741-750. doi: 10.21656/1000-0887.410142

Citation:

YIN Zihan, KANG Jing. Dispersive Quantization of 2D Linear Dispersive Equations[J]. Applied Mathematics and Mechanics, 2021, 42(7): 741-750. doi: 10.21656/1000-0887.410142

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Dispersive Quantization of 2D Linear Dispersive Equations

doi: 10.21656/1000-0887.410142

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)

Received Date: 2020-05-19
Rev Recd Date: 2020-05-23

Abstract

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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References(19)

References

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