On the persistence of spatial analyticity for generalized KdV equation with higher order dispersion

Persistence of spatial analyticity is studied for solutions of the generalized Korteweg-de Vries (KdV) equation with higher order dispersion (Formula presented.) where (Formula presented.), (Formula presented.) are integers. For a class of analytic initial data with a fixed radius of analyticity (Formula presented.), we show that the uniform radius of spatial analyticity (Formula presented.) of solutions at time (Formula presented.) cannot decay faster than (Formula presented.) as (Formula presented.). In particular, this improves a recent result due to Petronilho and Silva [Math. Nachr. 292 (2019), no. 9, 2032–2047] for the modified Kawahara equation ((Formula presented.), (Formula presented.)), where they obtained a decay rate of order (Formula presented.). Our proof relies on an approximate conservation law in a modified Gevrey spaces, local smoothing, and maximal function estimates.