We analyze the effect of phase-matched third-harmonic generation on the existence and stability of -dimensional bright and dark spatial solitary waves in optical media with a cubic (or Kerr) nonlinear response. We demonstrate that parametric coupling of the fundamental beam with the third harmonic leads to the existence of two-color solitary waves resembling those in a medium and that it can modify drastically the properties of solitary waves due to effective non-Kerr nonlinearities. In particular, we find a power threshold for the existence of two-frequency parametric bright solitons and also reveal the soliton multistability in a Kerr medium that becomes possible owing to a higher-order nonlinear phase shift caused by cascaded third-order processes. We also analyze dark solitary waves and their stabilities. We show that, in a certain parameter domain, parametric dark solitons may become unstable owing to the modulational instability of the supporting background or to other instability mechanisms caused by the parametric coupling between the harmonics.
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