Semiclassical wave packet dynamics for Hartree equations

Pei Cao (1) , Rémi Carles (2)

1 Department of Mathematical Science, Tsinghua University
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Pei Cao, Rémi Carles. Semiclassical wave packet dynamics for Hartree equations. Reviews in Mathematical Physics, 2011, 23 (9), pp.933-967. ⟨10.1142/S0129055X11004485⟩. ⟨hal-00559476v3⟩