Computability of Solutions of the Korteweg-de Vries Equation

In this paper we study computability of the solutions of the Korteweg-de Vries (KdV) equation u(t) + uu(x) + u(xxx) = 0. This is one of the open problems posted by Pour-El and Richards [25]. Based on Bourgain's new approach to the initial value problem for the KdV equation in the periodic case, we show that the periodic solution u(x, t) of the KdV equation is computable if the initial data is computable.