New asymptotic lower bound for the radius of analyticity of solutions to nonlinear Schrödinger equation

Abstract

In this paper, we show that the radius of analyticity [Formula: see text] of solutions to the one-dimensional nonlinear Schrödinger (NLS) equation [Formula: see text] is bounded from below by [Formula: see text] when [Formula: see text] and by [Formula: see text] when [Formula: see text] as [Formula: see text], given initial data that is analytic with fixed radius. This improves results obtained by Tesfahun [On the radius of spatial analyticity for cubic nonlinear Schrödinger equations, J. Differential Equations 263(11) (2017) 7496–7512] for [Formula: see text] and Ahn et al. [On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations, Discrete Contin. Dyn. Syst. 40(1) (2020) 423–439] for any odd integers [Formula: see text], where they obtained a decay rate [Formula: see text] for larger [Formula: see text]. The proof of our main theorems is based on a modified Gevrey space introduced in [T. T. Dufera, S. Mebrate and A. Tesfahun, On the persistence of spatial analyticity for the beam equation, J. Math. Anal. Appl. 509(2) (2022) 126001], the local smoothing effect, maximal function estimate of the Schrödinger propagator, a method of almost conservation law, Schrödinger admissibility and one-dimensional Sobolev embedding.