Asymptotic lower bound for the radius of spatial analyticity to solutions of KdV equation

It is shown that the uniform radius of spatial analyticity sigma(t) of solutions at time t to the KdV equation cannot decay faster than vertical bar t vertical bar(-4/3) as vertical bar t vertical bar ->infinity given initial data that is analytic with fixed radius sigma(0). This improves a recent result of Selberg and da Silva, where they proved a decay rate of vertical bar t vertical bar(-(4/3+epsilon)) for arbitrarily small positive epsilon. The main ingredients in the proof are almost conservation law for the solution to the KdV equation in space of analytic functions and space-time dyadic bilinear L-2 estimates associated with the KdV equation.