High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation
Abstract
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 solutions together with persistence of 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.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 9
- Pages
- 095007–095007
- Publication date
- 7 September 2026
- Language
- EN