Semiclassical wave packet dynamics for Hartree equations

TL;DR

This paper investigates semiclassical wave packet propagation in nonlinear nonlocal Schrödinger equations, constructing approximate solutions and analyzing their validity across different regimes, including superposition of wave packets.

Contribution

It introduces new methods for approximating wave packet solutions in nonlinear nonlocal Schrödinger equations and extends results to various critical regimes and superposition scenarios.

Findings

Approximate solutions are valid up to Ehrenfest time.

Results cover subcritical, critical, and supercritical cases.

Superposition principle for nonlinear wave packets is established.

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.