It is proved that formal power series solutions to the initial value problem , , with analytic data belong to the Gevrey class in time. However, if , the formal solution does not belong to the Gevrey class in time for , so it is not analytic in time. The proof is based on the estimation of a double sum of products of binomial coefficients.
Cite this article
Grzegorz Łysik, Non-Analyticity in Time of Solutions to the KdV Equation. Z. Anal. Anwend. 23 (2004), no. 1, pp. 67–93DOI 10.4171/ZAA/1188