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

In this paper, we show that the radius of analyticity sigma(t) of solutions to the one-dimensional nonlinear Schr odinger (NLS) equationi partial derivative tu+partial derivative 2xu=|u|p-1u is bounded from below by c|t|-23 when p>3 and by c|t|-45 when p=3 as |t|->+infinity, given initial data that is analytic with fixed radius. This improves results obtained byTesfahun [On the radius of spatial analyticity for cubic nonlinear Schr odinger equations,J. Differential Equations263(11) (2017) 7496-7512] forp=3andAhnet al.[Onthe radius of spatial analyticity for defocusing nonlinear Schrodinger equations,Discrete Contin. Dyn. Syst.40(1) (2020) 423-439] for any odd integersp>3, where theyobtained a decay rate sigma(t)>= c|t|-1for largert. 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 theSchr odinger propagator, a method of almost conservation law, Schr odinger admissibility and one-dimensional Sobolev embedding