Year: 2026
Type: preprint
Abstract: We study the semiclassical dynamics of solitary waves for the three-dimensional cubic--quintic nonlinear Schrödinger equation with an external potential. For initial data given by a modulated free ground state $P_ω$, we prove that the wave-packet center follows the associated classical Hamiltonian flow. For $ω\in\mathcal I$, we obtain qualitative persistence near the soliton orbit. Under the additional positive-slope condition $ω\in\mathcal I_+$, we establish an $O(\eps)$ approximation in the scaled $H^1$ norm on every fixed time interval. We also derive $O(\eps^2)$ concentration estimates for the mass, momentum, and center of mass.
Source: arXiv (Cornell University)
Authors: Ardila, Alex H., Carles, Rémi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214094983