Abstract
<p style='text-indent:20px;'>The nonlinear Schrödinger (NLS) equation is used to describe the envelopes of slowly modulated spatially and temporally oscillating wave packet-like solutions, which can be derived as a formal approximation equation of the quantum Euler-Poisson equation. In this paper, we rigorously justify such an approximation by taking a modified energy functional and a space-time resonance method to overcome the difficulties induced by the quadratic terms, resonance and quasilinearity.
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