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arXiv · 2602.19374

High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schr\"odinger equation

Jacek Jendrej·Tony Salvi
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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.

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Jacek Jendrej, Tony Salvi. 2026-02-22. High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schr\"odinger equation. https://arxiv.org/abs/2602.19374

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