Collective coordinate theory for light pulses in fibers: The reduced projection operators

► This work proposes a novel formalism of analysis of collective modes of light pulses. ► The formalism is based on projection operators of considerably reduced dimensions. ► The formalism allows deriving with a great ease the equations of collective modes. ► The formalism is decisive for analyzing complex dynamics with internal vibrations. ► We successfully apply it to the treatment the emission of radiation by a light pulse.