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arXiv · 2609.25648

Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential

Alex H. Ardila·Rémi Carles
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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.

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Alex H. Ardila, Rémi Carles. 2026-09-22. Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential. https://arxiv.org/abs/2609.25648

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