Noncommutative Korteweg-de-Vries Equation

We construct a deformation quantized version (ncKdV) of the KdV equation which possesses an infinite set of conserved densities. Solutions of the ncKdV are obtained from solutions of the KdV equation via a kind of Seiberg-Witten map. The ncKdV is related to a modified ncKdV equation by a noncommutative Miura transformation.