Propagation of radius of analyticity for solutions to a fourth‐order nonlinear Schrödinger equation

Abstract

We prove that the uniform radius of spatial analyticity of solution at time to the one‐dimensional fourth‐order nonlinear Schrödinger equation cannot decay faster than for large , given that the initial data are analytic with fixed radius . The main ingredients in the proof are a modified Gevrey space, a method of approximate conservation law, and a Strichartz estimate for free wave associated with the equation.