We construct a deformation quantized version (ncKdV) of the KdV equation wh
ich possesses an infinite set of conserved densities. Solutions of the ncKd
V equation are obtained from solutions of the KdV equation via a kind of Se
iberg-Witten map. The ncKdV equation is related to a modified ncKdV equatio
n by a noncommutative Miura transformation. (C) 2000 Elsevier Science B.V.
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