High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schr\"odinger equation
Analysis of PDEs
2026-02-24 v1 Quantum Physics
Abstract
We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we establish global existence of solution together with persistence of the localization of the associated profile. We further provide a rigorous derivation of the asymptotic expansion at arbitrary order of such solutions, taking into account long-range effects induced by the cubic component of the nonlinearity. Our analysis relies on the space-time resonance method.
Keywords
Cite
@article{arxiv.2602.19374,
title = {High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schr\"odinger equation},
author = {Jacek Jendrej and Tony Salvi},
journal= {arXiv preprint arXiv:2602.19374},
year = {2026}
}