Lower bounds on the radius of spatial analyticity for the fourth-order nonlinear Schrödinger equation with power-type nonlinearity

In this paper, we consider the initial value problem associated to the fourth-order nonlinear Schrödinger equation in the defocusing scenario :[Formula: see text] where [Formula: see text], [Formula: see text] be an odd integer, [Formula: see text], and the initial data g is analytic in a strip around the x-axis of the complex plane and has uniform radius of spatial analyticity [Formula: see text]. It is shown that the analyticity radius [Formula: see text] of solutions as time t goes to infinity does not decay faster than [Formula: see text]. Our strategy mainly relies on a method of approximate conservation law in a modified Gevrey spaces, biharmonic Schrödinger admissibility, Strichartz estimates and Sobolev embedding.