The Solution Operator of the Korteweg-de Vries Equation is Computable

The initial value problem of the Korteweg-de Vries (KdV) equation posted on the real line R: ut + uux + uxxx = 0, x ∈ R, t ∈ R u(x, 0) = ϕ(x), defines a nonlinear map KR from the space Hs(R) to the space C(R, Hs(R)) for any given real numbers s ≥ 0. In this paper we prove that the map KR is computable for any integer s ≥ 3.