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arXiv · 1511.00366

Long wavelength limit for the quantum Euler-Poisson equation

Huimin Liu·Xueke Pu
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Abstract

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.

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Huimin Liu, Xueke Pu. 2015-11-02. Long wavelength limit for the quantum Euler-Poisson equation. https://doi.org/10.1137/15m1046587

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