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Conformally compact and complete smooth solutions to the Strominger systemwith non vanishing flux, non-trivial instanton and non-constant dilaton usingthe first Pontrjagin form of the (-)-connection} on 6-dimensional non-Kaehlernilmanifold are presented. In the conformally compact case the dilaton isdetermined by the real slices of the elliptic Weierstrass function. The dilatonof non-compact complete solutions is given by the fundamental solution of theLaplacian on $R^4$.

Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton