A P ] 1 A ug 2 01 9 ON THE RADIUS OF SPATIAL ANALYTICITY FOR DEFOCUSING NONLINEAR SCHRÖDINGER EQUATIONS

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schrödinger equations iut + ∆u = |u|u, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time t cannot decay faster than 1/|t| as |t| → ∞. This extends the previous work of Tesfahun [19] for the cubic case p = 3 to the cases where p is any odd integer greater than 3.