Local well-posedness for the periodic Korteweg-de Vries equation in analytic Gevrey classes

Motivated by the work of Grujic and Kalisch, [Z. Grujic and H. Kalisch, Local well-posedness of the generalized Korteweg-de Vries equation in spaces of analytic functions , Differential and Integral Equations 15 (2002) 1325--1334], we prove the local well-posedness for the periodic KdV equation in spaces of periodic functions analytic on a strip around the real axis without shrinking the width of the strip in time.