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Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential
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 Pω, we prove that the wave-packet center follows the associated classical Hamiltonian flow. For ω∈ℐ, we obtain qualitative persistence near the soliton orbit. Under the additional positive-slope condition ω∈ℐ+, we establish an O(eps) approximation in the scaled H1 norm on every fixed time interval. We also derive O(eps2) concentration estimates for the mass, momentum, and center of mass.
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BibTeX
@misc{ardila2026soliton,
title = {{Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential}},
author = {Alex H. Ardila and Rémi Carles},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25648},
eprint = {2609.25648},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25648},
}
RIS
TY - UNPB
TI - Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential
AU - Alex H. Ardila
AU - Rémi Carles
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25648
UR - https://arxiv.org/abs/2609.25648
AB - 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∈ℐ, we obtain qualitative persistence near the soliton orbit. Under the additional positive-slope condition ω∈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.
ER -