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It is proved that the formal power series solutions to the initial value problem @tu = @ 3 xu +@x(u 2 ), u(0;x) = '(x), where ' is analytic belong to the Gevrey class G 2 in time. However, if '(x) = 1=(1 +x 2 ), the solution does not belong to the Gevrey class G s in time for 0 s < 2. The proof is based on the estimation of a double sum of products of binomial coecients. 1. Introduction. We consider the characteristic Cauchy problem for the Korteweg- de Vries equation (1) @tu = @ 3 xu +@x(u 2 ); u(0;x) = '(x):

Non-Analyticity in Time of Solutions to the KdV Equation