Lower bounds on the radius of analyticity for a system of modified KdV equations

The initial value problem for a system of modified Korteweg-deVries equations with data that are analytic on R and having uniform radius of analyticity r0 is studied. After proving an analytic version of known trilinear estimates in Sobolev spaces, local well-posedness is established and persistence of the radius of spatial analyticity is shown till some time T0. Then, for time t≥T0 it is proved that the radius of spatial analyticity is bounded from below by ct−(2+ε), for any ε>0.