Long-Time Dynamics of Small Solutions to 1d Cubic Nonlinear Schrödinger Equations with A Trapping Potential
Abstract
Abstract In this paper, we analyze the long-time dynamics of small solutions to the 1 d cubic nonlinear Schrödinger equation (NLS) with a trapping potential. We show that every small solution decomposes into a small solitary wave and a radiation term exhibiting modified scattering. Our analysis also establishes the long-time behavior of solutions to perturbations of the integrable cubic NLS in the presence of solitons.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Photonic Systems
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Communications in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 407
- Issue
- 6
- Publication date
- 2 May 2026
- Language
- EN