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

In this paper, we show that the radius of analyticity σ (t) of solutions to the one-dimensional nonlinear Schrödinger (NLS) equation i ∂ t u + ∂ x 2 u = | u | p − 1 u is bounded from below by c | t | − 2 3 when p > 3 and by c | t | − 4 5 when p = 3 as | t | → + ∞ , 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 p = 3 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 p > 3 , where they obtained a decay rate σ (t) ≥ c | t | − 1 for larger t. 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. [ABSTRACT FROM AUTHOR]