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The authors develop and apply a novel group-theoretical approach for studying the coherent dynamics of ultrashort pulse propagation in nonlinear optical waveguides and passive semiconductor microresonators. The resonant nonlinearity is modeled by a degenerate three-level system of saturable absorbers in order to allow for a two-dimensional medium polarization. The resulting Maxwell-pseudospin equations are solved in the time domain using the finite-difference time-domain method. Conditions of onset of the self-induced transparency (SIT) regime of propagation are investigated. Numerical evidence of multidimensional solitons localized both in space and in time is given for the planar optical waveguides. Pattern formation and cavity SIT-soliton formation are demonstrated for a passive semiconductor microcavity filled with saturable absorbers.