Long wavelength limit for the quantum Euler-Poisson equation

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.

36pages

References in corpus (3)

• KdV limit of the Euler-Poisson system
• From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov
• Quasineutral limit of the Euler-Poisson equation for a cold, ion-acoustic plasma