Modulation approximation for the quantum Euler-Poisson equation (Q2033795)

In this paper, the authors consider the bi-polar Euler-Poisson equations with quantum effect. The main issue of the paper is to consider the modulation approximation for the Euler-Poisson equations, which is a kind of nonlinear Schrödinger equation. The authors make a rigorous justification of such an approximation by taking a modified energy functional and a space-time resonance method.