Semiclassical wave packet dynamics for Hartree equations

Details Semiclassical wave packet dynamics for Hartree equations Semiclassical wave packet dynamics for Hartree equations

2011-01-25

arxiv.org/abs/1101.4851v3

Reviews in Mathematical Physics 23, 9 (2011) 933-967

Physics

Mathematical Physics

28 pages. Some errors fixed in Section 2.7

Scientific paper

10.1142/S0129055X11004485

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.

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