Noncommutative Korteweg-de-Vries Equation
Aristophanes Dimakis, Folkert Muller-Hoissen
Abstract
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.
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