On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well-posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data u0(x) that can be extended as holomorphic functions in a strip around the x-axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity r(t) given by r(t)>= ct-(4+delta), where delta>0 can be taken arbitrarily small and c is a positive constant.