Spatial analyticity of solutions to nonlinear dispersive PDE

Abstract

Given a nonlinear dispersive PDE, for example the KdV equation, we consider the Cauchy problem with real analytic initial data. For data with a uniform radius of analyticity, we are interested in obtaining lower bounds on the radius of analyticity at later times. A rather general approach to this problem is presented, based on Bourgain’s Fourier restriction norm method. Applications to the KdV equation (periodic and non-periodic) and the Dirac–Klein–Gordon equations are discussed.