Semiclassical Wave Packet Dynamics For Nonlinear Schrödinger Equations with Harmonic Potentials

We propose an approximate Hamiltonian dynamics for the Gross--Pitaevskii equation $i\hbarψ_t = -\frac{\hbar^2}{2m}Δψ+ V(x)ψ+ \hbar^2 λ|ψ|^2ψ$ with harmonic potential $V(x)$ and $x\in\mathbb{R}^d$. We do this by extending the Gaussian ansatz of Perez-Garcia et al.~(Phys.~Rev.~A 56, 1424 (1997)) to th