TY - JOUR
T1 - Modulation approximation for the quantum euler-poisson equation
AU - Bian, Dongfen
AU - Liu, Huimin
AU - Pu, Xueke
N1 - Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.
PY - 2021/8
Y1 - 2021/8
N2 - The nonlinear Schrödinger (NLS) equation is used to describe the envelopes of slowly modulated spatially and temporally oscillating wave packetlike 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.
AB - The nonlinear Schrödinger (NLS) equation is used to describe the envelopes of slowly modulated spatially and temporally oscillating wave packetlike 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.
KW - Euler- Poisson equation
KW - Modified energy
KW - Modulation approximation
KW - Nonlinear Schrödinger equation
KW - Space-time resonance
UR - https://www.scopus.com/pages/publications/85108536551
U2 - 10.3934/dcdsb.2020292
DO - 10.3934/dcdsb.2020292
M3 - Article
AN - SCOPUS:85108536551
SN - 1531-3492
VL - 26
SP - 4375
EP - 4405
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 8
ER -