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Long Wavelength Limit for the Quantum Euler-Poisson Equation
LIU Hui-Min #,PU Xue-Ke *
College of Mathematics and Statistics, Chongqing University, Chongqing 401331
*Correspondence author
#Submitted by
Subject:
Funding: NSFC （No.11471057）, Natural Science Foundation Project of CQ CSTC （No.cstc2014jcyjA50020）
Opened online:25 April 2016
Accepted by: none
Citation: LIU Hui-Min,PU Xue-Ke.Long Wavelength Limit for the Quantum Euler-Poisson Equation[OL]. [25 April 2016] http://en.paper.edu.cn/en_releasepaper/content/4684352
 
 
In this paper, we consider the long wavelength limit for the quantum Euler-Poisson equation. Under the Gardner-Morikawa transform, we derive the quantum Korteweg-de Vries (KdV) equation by a singular perturbation method. We show that the KdV dynamics can be seen at time interval of order $O(epsilon^{-3/2})$. When the nondimensional quantum parameter $H=2$, it reduces to the inviscid Burgers equation.
Keywords:quantum effect；Euler-Poission equations; plasma
 
 
 

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