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We promote the open-closed string map, originally formulated by Seiberg \& Witten, to a solution generating technique in generalized supergravity. The entire prescription hinges on knowledge of an antisymmetric bivector $\Theta$, which is specified by the equations of motion. In the cases we study, the equations of motion reproduce the Classical Yang-Baxter equation and $\Theta$ is the most general $r$-matrix solution. Our work opens a new window on the relation between integrable models, supergravity and noncommutativity in string theory.
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