Semiclassical wave packet dynamics for Hartree equations
Mathematical Physics
2012-01-16 v3 Analysis of PDEs
math.MP
Abstract
We study the propagation of wave packets for nonlinear nonlocal Schrodinger equations in the semi-classical limit. When the kernel is smooth, we construct approximate solutions for the wave functions in subcritical, critical and supercritical cases (in terms of the size of the initial data). The validity of the approximation is proved up to Ehrenfest time. For homogeneous kernels, we establish similar results in subcritical and critical cases. Nonlinear superposition principle for two nonlinear wave packets is also considered.
Cite
@article{arxiv.1101.4851,
title = {Semiclassical wave packet dynamics for Hartree equations},
author = {Pei Cao and Rémi Carles},
journal= {arXiv preprint arXiv:1101.4851},
year = {2012}
}
Comments
28 pages. Some errors fixed in Section 2.7