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The initial value problem of the Korteweg-de Vries (KdV) equation posted on the real line R: defines a nonlinear map K R from the space H s (R) to the space C(R, H s (R)) for any given real numbers s ≥ 0. In this paper we prove that the map K R is computable for any integer s ≥ 3. 1doi:10.1016/s1571-0661(04)80389-x fatcat:a7yoo6ldf5dqpfoirpqecods7m