| Abstract : This will be an attempt to give a brief survey of the curent state of affairs in the study of spatial analyticity properties of nonlinear dispersive wave equations--in particular, the generalized Korteweg-de Vries equation and the derivative Schrodinger equation. Both of these models have a spatial derivative in the nonlinear term causing the so called "derivative loss" in the model. It turns out that analytic Bourgain-Gevrey spaces provide a medium in which dispersive smoothing can be efficiently exploited compensating for the derivative loss. Both local and global-in-time results will be presented. |