High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation

• URL: http://arxiv.org/abs/2602.19374v1
• Date: Sun, 22 Feb 2026 22:59:23 GMT
• Title: High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation
• Authors: Jacek Jendrej, Tony Salvi,
• Abstract summary: We investigate the global well-posedness and modified scattering for the one-dimensional Schrdinger equation with gauge-invariant nonlinearity.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the global well-posedness and modified scattering for the one-dimensional Schrödinger 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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